id	sid	tid	token	lemma	pos
bibechana-5700	1	1	microsoft	microsoft	PROPN
bibechana-5700	1	2	word	word	PROPN
bibechana-5700	1	3	nagendra	nagendra	PROPN
bibechana-5700	1	4	sir.doc	sir.doc	PROPN
bibechana-5700	1	5	g.k	g.k	PROPN
bibechana-5700	1	6	.	.	PROPN
bibechana-5700	1	7	palei	palei	PROPN
bibechana-5700	1	8	and	and	CCONJ
bibechana-5700	1	9	n.p	n.p	PROPN
bibechana-5700	1	10	.	.	PROPN
bibechana-5700	1	11	sah	sah	PROPN
bibechana-5700	1	12	/	/	SYM
bibechana-5700	1	13	bibechana	bibechana	PROPN
bibechana-5700	1	14	8	8	NUM
bibechana-5700	1	15	(	(	PUNCT
bibechana-5700	1	16	2012	2012	NUM
bibechana-5700	1	17	)	)	PUNCT
bibechana-5700	1	18	127	127	NUM
bibechana-5700	1	19	-	-	SYM
bibechana-5700	1	20	130	130	NUM
bibechana-5700	1	21	:	:	PUNCT
bibechana-5700	1	22	bmhss	bmhss	PROPN
bibechana-5700	1	23	,	,	PUNCT
bibechana-5700	1	24	p.127	p.127	PROPN
bibechana-5700	1	25	bibechana	bibechana	NOUN
bibechana-5700	1	26	a	a	DET
bibechana-5700	1	27	multidisciplinary	multidisciplinary	ADJ
bibechana-5700	1	28	journal	journal	NOUN
bibechana-5700	1	29	of	of	ADP
bibechana-5700	1	30	science	science	NOUN
bibechana-5700	1	31	,	,	PUNCT
bibechana-5700	1	32	technology	technology	NOUN
bibechana-5700	1	33	and	and	CCONJ
bibechana-5700	1	34	mathematics	mathematic	NOUN
bibechana-5700	1	35	issn	issn	VERB
bibechana-5700	1	36	2091	2091	NUM
bibechana-5700	1	37	-	-	SYM
bibechana-5700	1	38	0762	0762	NUM
bibechana-5700	1	39	(	(	PUNCT
bibechana-5700	1	40	online	online	ADJ
bibechana-5700	1	41	)	)	PUNCT
bibechana-5700	1	42	journal	journal	NOUN
bibechana-5700	1	43	homepage	homepage	NOUN
bibechana-5700	1	44	:	:	PUNCT
bibechana-5700	1	45	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-5700	1	46	foundations	foundation	NOUN
bibechana-5700	1	47	of	of	ADP
bibechana-5700	1	48	the	the	DET
bibechana-5700	1	49	fredholm	fredholm	NOUN
bibechana-5700	1	50	alternative	alternative	NOUN
bibechana-5700	1	51	theorem	theorem	ADJ
bibechana-5700	1	52	,	,	PUNCT
bibechana-5700	1	53	equicontinuous	equicontinuous	ADJ
bibechana-5700	1	54	operators	operator	NOUN
bibechana-5700	1	55	and	and	CCONJ
bibechana-5700	1	56	completely	completely	ADV
bibechana-5700	1	57	continuous	continuous	ADJ
bibechana-5700	1	58	operators	operator	NOUN
bibechana-5700	1	59	g.k	g.k	PROPN
bibechana-5700	1	60	.	.	PROPN
bibechana-5700	1	61	palei	palei	PROPN
bibechana-5700	1	62	1	1	NUM
bibechana-5700	1	63	,	,	PUNCT
bibechana-5700	1	64	n.p	n.p	PROPN
bibechana-5700	1	65	.	.	PROPN
bibechana-5700	1	66	sah	sah	PROPN
bibechana-5700	1	67	2	2	NUM
bibechana-5700	1	68	*	*	SYM
bibechana-5700	1	69	1	1	NUM
bibechana-5700	1	70	department	department	NOUN
bibechana-5700	1	71	of	of	ADP
bibechana-5700	1	72	mathematics	mathematics	PROPN
bibechana-5700	1	73	,	,	PUNCT
bibechana-5700	1	74	b.n	b.n	PROPN
bibechana-5700	1	75	.	.	PROPN
bibechana-5700	1	76	college	college	PROPN
bibechana-5700	1	77	,	,	PUNCT
bibechana-5700	1	78	patna	patna	PROPN
bibechana-5700	1	79	university	university	PROPN
bibechana-5700	1	80	,	,	PUNCT
bibechana-5700	1	81	patna	patna	PROPN
bibechana-5700	1	82	,	,	PUNCT
bibechana-5700	1	83	india	india	PROPN
bibechana-5700	1	84	2	2	NUM
bibechana-5700	1	85	department	department	NOUN
bibechana-5700	1	86	of	of	ADP
bibechana-5700	1	87	mathematics	mathematics	PROPN
bibechana-5700	1	88	m.m.a.m	m.m.a.m	PROPN
bibechana-5700	1	89	.	.	PUNCT
bibechana-5700	2	1	campus	campus	PROPN
bibechana-5700	2	2	(	(	PUNCT
bibechana-5700	2	3	tribhuvan	tribhuvan	PROPN
bibechana-5700	2	4	university	university	PROPN
bibechana-5700	2	5	)	)	PUNCT
bibechana-5700	2	6	,	,	PUNCT
bibechana-5700	2	7	biratnagar	biratnagar	NOUN
bibechana-5700	2	8	,	,	PUNCT
bibechana-5700	2	9	nepal	nepal	ADJ
bibechana-5700	2	10	article	article	NOUN
bibechana-5700	2	11	history	history	NOUN
bibechana-5700	2	12	:	:	PUNCT
bibechana-5700	2	13	received	receive	VERB
bibechana-5700	2	14	25	25	NUM
bibechana-5700	2	15	july	july	PROPN
bibechana-5700	2	16	,	,	PUNCT
bibechana-5700	2	17	2011	2011	NUM
bibechana-5700	2	18	;	;	PUNCT
bibechana-5700	2	19	accepted	accept	VERB
bibechana-5700	2	20	27	27	NUM
bibechana-5700	2	21	nov	nov	NOUN
bibechana-5700	2	22	.	.	PROPN
bibechana-5700	2	23	,	,	PUNCT
bibechana-5700	2	24	2011	2011	NUM
bibechana-5700	2	25	abstract	abstract	NOUN
bibechana-5700	2	26	the	the	DET
bibechana-5700	2	27	fredholm	fredholm	NOUN
bibechana-5700	2	28	alternative	alternative	NOUN
bibechana-5700	2	29	theorem	theorem	NOUN
bibechana-5700	2	30	gives	give	VERB
bibechana-5700	2	31	the	the	DET
bibechana-5700	2	32	notion	notion	NOUN
bibechana-5700	2	33	of	of	ADP
bibechana-5700	2	34	bounded	bounded	ADJ
bibechana-5700	2	35	and	and	CCONJ
bibechana-5700	2	36	continuous	continuous	ADJ
bibechana-5700	2	37	operator	operator	NOUN
bibechana-5700	2	38	which	which	PRON
bibechana-5700	2	39	makes	make	VERB
bibechana-5700	2	40	a	a	DET
bibechana-5700	2	41	family	family	NOUN
bibechana-5700	2	42	f	f	NOUN
bibechana-5700	2	43	of	of	ADP
bibechana-5700	2	44	elements	element	NOUN
bibechana-5700	2	45	of	of	ADP
bibechana-5700	2	46	c[a	c[a	NUM
bibechana-5700	2	47	,	,	PUNCT
bibechana-5700	2	48	b	b	X
bibechana-5700	2	49	]	]	X
bibechana-5700	2	50	bounded	bound	VERB
bibechana-5700	2	51	and	and	CCONJ
bibechana-5700	2	52	equicontinuous	equicontinuous	ADJ
bibechana-5700	2	53	.	.	PUNCT
bibechana-5700	3	1	a	a	DET
bibechana-5700	3	2	continuous	continuous	ADJ
bibechana-5700	3	3	operator	operator	NOUN
bibechana-5700	3	4	of	of	ADP
bibechana-5700	3	5	finite	finite	PROPN
bibechana-5700	3	6	rank	rank	NOUN
bibechana-5700	3	7	is	be	AUX
bibechana-5700	3	8	completely	completely	ADV
bibechana-5700	3	9	continuous	continuous	ADJ
bibechana-5700	3	10	but	but	CCONJ
bibechana-5700	3	11	every	every	DET
bibechana-5700	3	12	continuous	continuous	ADJ
bibechana-5700	3	13	operator	operator	NOUN
bibechana-5700	3	14	is	be	AUX
bibechana-5700	3	15	not	not	PART
bibechana-5700	3	16	completely	completely	ADV
bibechana-5700	3	17	continuous	continuous	ADJ
bibechana-5700	3	18	operator	operator	NOUN
bibechana-5700	3	19	.	.	PUNCT
bibechana-5700	4	1	keywords	keyword	NOUN
bibechana-5700	4	2	:	:	PUNCT
bibechana-5700	4	3	arzela	arzela	PROPN
bibechana-5700	4	4	-	-	PUNCT
bibechana-5700	4	5	ascoli	ascoli	PROPN
bibechana-5700	4	6	's	's	PART
bibechana-5700	4	7	theorem	theorem	ADJ
bibechana-5700	4	8	;	;	PUNCT
bibechana-5700	4	9	completely	completely	ADV
bibechana-5700	4	10	continuous	continuous	ADJ
bibechana-5700	4	11	;	;	PUNCT
bibechana-5700	4	12	equicontinuous	equicontinuous	ADJ
bibechana-5700	4	13	and	and	CCONJ
bibechana-5700	4	14	fredholm	fredholm	ADJ
bibechana-5700	4	15	alternative	alternative	NOUN
bibechana-5700	4	16	theorem	theorem	NOUN
bibechana-5700	4	17	1	1	NUM
bibechana-5700	4	18	.	.	PUNCT
bibechana-5700	4	19	introduction	introduction	NOUN
bibechana-5700	4	20	if	if	SCONJ
bibechana-5700	4	21	x	x	PRON
bibechana-5700	4	22	be	be	AUX
bibechana-5700	4	23	a	a	DET
bibechana-5700	4	24	liner	liner	NOUN
bibechana-5700	4	25	space	space	NOUN
bibechana-5700	4	26	over	over	ADP
bibechana-5700	4	27	the	the	DET
bibechana-5700	4	28	field	field	NOUN
bibechana-5700	4	29	φ	φ	PROPN
bibechana-5700	4	30	of	of	ADP
bibechana-5700	4	31	real	real	ADJ
bibechana-5700	4	32	or	or	CCONJ
bibechana-5700	4	33	complex	complex	ADJ
bibechana-5700	4	34	numbers	number	NOUN
bibechana-5700	4	35	,	,	PUNCT
bibechana-5700	4	36	then	then	ADV
bibechana-5700	4	37	the	the	DET
bibechana-5700	4	38	set	set	NOUN
bibechana-5700	4	39	of	of	ADP
bibechana-5700	4	40	all	all	DET
bibechana-5700	4	41	linear	linear	ADJ
bibechana-5700	4	42	transformations	transformation	NOUN
bibechana-5700	4	43	t	t	NOUN
bibechana-5700	4	44	from	from	ADP
bibechana-5700	4	45	x	x	PUNCT
bibechana-5700	4	46	into	into	ADP
bibechana-5700	4	47	itself	itself	PRON
bibechana-5700	4	48	form	form	VERB
bibechana-5700	4	49	a	a	DET
bibechana-5700	4	50	linear	linear	ADJ
bibechana-5700	4	51	space	space	NOUN
bibechana-5700	4	52	l(x	l(x	NOUN
bibechana-5700	4	53	)	)	PUNCT
bibechana-5700	4	54	on	on	ADP
bibechana-5700	4	55	x.	x.	NOUN
bibechana-5700	4	56	the	the	DET
bibechana-5700	4	57	linear	linear	PROPN
bibechana-5700	4	58	subspace	subspace	NOUN
bibechana-5700	4	59	n(t)=	n(t)=	NOUN
bibechana-5700	4	60	{	{	PUNCT
bibechana-5700	4	61	,	,	PUNCT
bibechana-5700	4	62	0}x	0}x	NUM
bibechana-5700	4	63	x	x	PUNCT
bibechana-5700	4	64	tx∈	tx∈	PROPN
bibechana-5700	4	65	=	=	PUNCT
bibechana-5700	4	66	is	be	AUX
bibechana-5700	4	67	called	call	VERB
bibechana-5700	4	68	the	the	DET
bibechana-5700	4	69	null	null	ADJ
bibechana-5700	4	70	space	space	NOUN
bibechana-5700	4	71	of	of	ADP
bibechana-5700	4	72	t	t	PROPN
bibechana-5700	4	73	and	and	CCONJ
bibechana-5700	4	74	b(t)=	b(t)=	NOUN
bibechana-5700	4	75	{	{	PUNCT
bibechana-5700	4	76	}	}	PUNCT
bibechana-5700	4	77	:	:	PUNCT
bibechana-5700	4	78	,	,	PUNCT
bibechana-5700	4	79	y	y	PROPN
bibechana-5700	4	80	x	x	VERB
bibechana-5700	4	81	tx	tx	PROPN
bibechana-5700	4	82	y	y	PROPN
bibechana-5700	5	1	x	x	X
bibechana-5700	5	2	x∈	x∈	PROPN
bibechana-5700	5	3	=	=	PUNCT
bibechana-5700	5	4	∈	∈	PROPN
bibechana-5700	5	5	is	be	AUX
bibechana-5700	5	6	called	call	VERB
bibechana-5700	5	7	the	the	DET
bibechana-5700	5	8	image	image	NOUN
bibechana-5700	5	9	space	space	NOUN
bibechana-5700	5	10	of	of	ADP
bibechana-5700	5	11	t.	t.	PROPN
bibechana-5700	5	12	the	the	DET
bibechana-5700	5	13	fredhlom	fredhlom	ADJ
bibechana-5700	5	14	alternative	alternative	ADJ
bibechana-5700	5	15	theorem	theorem	NOUN
bibechana-5700	5	16	is	be	AUX
bibechana-5700	5	17	based	base	VERB
bibechana-5700	5	18	on	on	ADP
bibechana-5700	5	19	the	the	DET
bibechana-5700	5	20	linear	linear	PROPN
bibechana-5700	5	21	algebra	algebra	NOUN
bibechana-5700	5	22	.	.	PUNCT
bibechana-5700	6	1	i.e.	i.e.	X
bibechana-5700	6	2	if	if	SCONJ
bibechana-5700	6	3	dimx	dimx	NOUN
bibechana-5700	6	4	<	<	X
bibechana-5700	6	5	∞	∞	PROPN
bibechana-5700	6	6	and	and	CCONJ
bibechana-5700	6	7	t∈l(x	t∈l(x	NOUN
bibechana-5700	6	8	)	)	PUNCT
bibechana-5700	6	9	,	,	PUNCT
bibechana-5700	6	10	then	then	ADV
bibechana-5700	6	11	the	the	DET
bibechana-5700	6	12	following	follow	VERB
bibechana-5700	6	13	alternative	alternative	NOUN
bibechana-5700	6	14	holds	hold	VERB
bibechana-5700	6	15	:	:	PUNCT
bibechana-5700	6	16	either	either	CCONJ
bibechana-5700	6	17	the	the	DET
bibechana-5700	6	18	equation	equation	NOUN
bibechana-5700	6	19	tx	tx	VERB
bibechana-5700	6	20	=	=	SYM
bibechana-5700	6	21	0	0	PROPN
bibechana-5700	6	22	has	have	VERB
bibechana-5700	6	23	only	only	ADV
bibechana-5700	6	24	the	the	DET
bibechana-5700	6	25	trivial	trivial	ADJ
bibechana-5700	6	26	solution	solution	NOUN
bibechana-5700	6	27	x	x	PUNCT
bibechana-5700	7	1	=	=	SYM
bibechana-5700	7	2	0	0	NUM
bibechana-5700	8	1	in	in	ADP
bibechana-5700	8	2	which	which	DET
bibechana-5700	8	3	case	case	NOUN
bibechana-5700	8	4	the	the	DET
bibechana-5700	8	5	equation	equation	NOUN
bibechana-5700	8	6	tx	tx	PROPN
bibechana-5700	8	7	=	=	SYM
bibechana-5700	8	8	y	y	PROPN
bibechana-5700	8	9	has	have	VERB
bibechana-5700	8	10	a	a	DET
bibechana-5700	8	11	unique	unique	ADJ
bibechana-5700	8	12	solution	solution	NOUN
bibechana-5700	8	13	x∈x	x∈x	NOUN
bibechana-5700	8	14	for	for	ADP
bibechana-5700	8	15	arbitrary	arbitrary	ADJ
bibechana-5700	8	16	y∈x	y∈x	NOUN
bibechana-5700	8	17	.	.	PUNCT
bibechana-5700	9	1	or	or	CCONJ
bibechana-5700	9	2	the	the	DET
bibechana-5700	9	3	equation	equation	NOUN
bibechana-5700	9	4	tx	tx	PROPN
bibechana-5700	9	5	=	=	SYM
bibechana-5700	9	6	0	0	PROPN
bibechana-5700	9	7	has	have	VERB
bibechana-5700	9	8	nontrivial	nontrivial	ADJ
bibechana-5700	9	9	solutions	solution	NOUN
bibechana-5700	9	10	in	in	ADP
bibechana-5700	9	11	which	which	DET
bibechana-5700	9	12	case	case	NOUN
bibechana-5700	9	13	the	the	DET
bibechana-5700	9	14	equation	equation	NOUN
bibechana-5700	9	15	tx	tx	PROPN
bibechana-5700	10	1	=	=	PUNCT
bibechana-5700	10	2	y	y	PROPN
bibechana-5700	10	3	is	be	AUX
bibechana-5700	10	4	not	not	PART
bibechana-5700	10	5	always	always	ADV
bibechana-5700	10	6	solvable	solvable	ADJ
bibechana-5700	10	7	for	for	ADP
bibechana-5700	10	8	each	each	DET
bibechana-5700	10	9	y∈x	y∈x	NOUN
bibechana-5700	10	10	.	.	PUNCT
bibechana-5700	11	1	the	the	DET
bibechana-5700	11	2	above	above	ADJ
bibechana-5700	11	3	alternative	alternative	ADJ
bibechana-5700	11	4	theorem	theorem	NOUN
bibechana-5700	11	5	does	do	AUX
bibechana-5700	11	6	not	not	PART
bibechana-5700	11	7	hold	hold	VERB
bibechana-5700	11	8	for	for	ADP
bibechana-5700	11	9	infinite	infinite	ADJ
bibechana-5700	11	10	dimensional	dimensional	ADJ
bibechana-5700	11	11	vector	vector	NOUN
bibechana-5700	11	12	spaces	space	NOUN
bibechana-5700	11	13	.	.	PUNCT
bibechana-5700	12	1	for	for	ADP
bibechana-5700	12	2	this	this	PRON
bibechana-5700	12	3	,	,	PUNCT
bibechana-5700	12	4	consider	consider	VERB
bibechana-5700	12	5	the	the	DET
bibechana-5700	12	6	vector	vector	NOUN
bibechana-5700	12	7	space	space	NOUN
bibechana-5700	12	8	(	(	PUNCT
bibechana-5700	12	9	s	s	NOUN
bibechana-5700	12	10	)	)	PUNCT
bibechana-5700	12	11	of	of	ADP
bibechana-5700	12	12	all	all	DET
bibechana-5700	12	13	sequences	sequence	NOUN
bibechana-5700	12	14	of	of	ADP
bibechana-5700	12	15	real	real	ADJ
bibechana-5700	12	16	or	or	CCONJ
bibechana-5700	12	17	complex	complex	ADJ
bibechana-5700	12	18	numbers	number	NOUN
bibechana-5700	12	19	.	.	PUNCT
bibechana-5700	13	1	the	the	DET
bibechana-5700	13	2	map	map	NOUN
bibechana-5700	13	3	defined	define	VERB
bibechana-5700	13	4	on	on	ADP
bibechana-5700	13	5	(	(	PUNCT
bibechana-5700	13	6	s	s	X
bibechana-5700	13	7	)	)	PUNCT
bibechana-5700	13	8	by	by	ADP
bibechana-5700	13	9	t(x1	t(x1	NOUN
bibechana-5700	13	10	,	,	PUNCT
bibechana-5700	13	11	x2	x2	PROPN
bibechana-5700	13	12	,	,	PUNCT
bibechana-5700	13	13	>	>	PUNCT
bibechana-5700	13	14	)	)	PUNCT
bibechana-5700	13	15	=	=	SYM
bibechana-5700	13	16	(	(	PUNCT
bibechana-5700	13	17	0	0	NUM
bibechana-5700	13	18	,	,	PUNCT
bibechana-5700	13	19	x1	x1	PROPN
bibechana-5700	13	20	,	,	PUNCT
bibechana-5700	13	21	x2	x2	PROPN
bibechana-5700	13	22	>	>	X
bibechana-5700	13	23	>	>	X
bibechana-5700	13	24	>	>	X
bibechana-5700	13	25	..	..	PUNCT
bibechana-5700	13	26	)	)	PUNCT
bibechana-5700	13	27	is	be	AUX
bibechana-5700	13	28	one	one	NUM
bibechana-5700	13	29	to	to	ADP
bibechana-5700	13	30	one	one	NUM
bibechana-5700	13	31	and	and	CCONJ
bibechana-5700	13	32	onto	onto	ADP
bibechana-5700	13	33	,	,	PUNCT
bibechana-5700	13	34	hence	hence	ADV
bibechana-5700	13	35	t(x1	t(x1	NOUN
bibechana-5700	13	36	,	,	PUNCT
bibechana-5700	13	37	x2	x2	PROPN
bibechana-5700	13	38	,	,	PUNCT
bibechana-5700	13	39	>	>	X
bibechana-5700	13	40	>	>	X
bibechana-5700	13	41	.	.	PUNCT
bibechana-5700	13	42	)	)	PUNCT
bibechana-5700	14	1	=	=	SYM
bibechana-5700	14	2	0	0	PUNCT
bibechana-5700	14	3	has	have	VERB
bibechana-5700	14	4	the	the	DET
bibechana-5700	14	5	only	only	ADJ
bibechana-5700	14	6	trivial	trivial	ADJ
bibechana-5700	14	7	solution	solution	NOUN
bibechana-5700	14	8	x1	x1	NOUN
bibechana-5700	15	1	=	=	PUNCT
bibechana-5700	15	2	x2	x2	PROPN
bibechana-5700	15	3	=	=	PUNCT
bibechana-5700	16	1	>	>	PUNCT
bibechana-5700	16	2	>	>	X
bibechana-5700	16	3	>	>	X
bibechana-5700	16	4	=	=	PUNCT
bibechana-5700	16	5	0	0	PUNCT
bibechana-5700	17	1	but	but	CCONJ
bibechana-5700	17	2	still	still	ADV
bibechana-5700	17	3	the	the	DET
bibechana-5700	17	4	equation	equation	NOUN
bibechana-5700	17	5	tx	tx	PROPN
bibechana-5700	18	1	=	=	PUNCT
bibechana-5700	18	2	y	y	PROPN
bibechana-5700	18	3	is	be	AUX
bibechana-5700	18	4	not	not	PART
bibechana-5700	18	5	solvable	solvable	ADJ
bibechana-5700	18	6	for	for	ADP
bibechana-5700	18	7	all	all	DET
bibechana-5700	18	8	y∈(s	y∈(s	NOUN
bibechana-5700	18	9	)	)	PUNCT
bibechana-5700	18	10	whose	whose	DET
bibechana-5700	18	11	first	first	ADJ
bibechana-5700	18	12	component	component	NOUN
bibechana-5700	18	13	is	be	AUX
bibechana-5700	18	14	zero	zero	NUM
bibechana-5700	18	15	.	.	PUNCT
bibechana-5700	19	1	fredhlom	fredhlom	NOUN
bibechana-5700	19	2	has	have	AUX
bibechana-5700	19	3	proved	prove	VERB
bibechana-5700	19	4	in	in	ADP
bibechana-5700	19	5	his	his	PRON
bibechana-5700	19	6	work	work	NOUN
bibechana-5700	19	7	(	(	PUNCT
bibechana-5700	19	8	1900	1900	NUM
bibechana-5700	19	9	-	-	SYM
bibechana-5700	19	10	1903	1903	NUM
bibechana-5700	19	11	)	)	PUNCT
bibechana-5700	19	12	that	that	SCONJ
bibechana-5700	19	13	the	the	DET
bibechana-5700	19	14	alternative	alternative	NOUN
bibechana-5700	19	15	theorem[4	theorem[4	PRON
bibechana-5700	19	16	]	]	PUNCT
bibechana-5700	19	17	is	be	AUX
bibechana-5700	19	18	valid	valid	ADJ
bibechana-5700	19	19	for	for	ADP
bibechana-5700	19	20	a	a	DET
bibechana-5700	19	21	certain	certain	ADJ
bibechana-5700	19	22	class	class	NOUN
bibechana-5700	19	23	of	of	ADP
bibechana-5700	19	24	linear	linear	ADJ
bibechana-5700	19	25	integral	integral	ADJ
bibechana-5700	19	26	equations	equation	NOUN
bibechana-5700	19	27	.	.	PUNCT
bibechana-5700	20	1	g.k	g.k	PROPN
bibechana-5700	20	2	.	.	PROPN
bibechana-5700	20	3	palei	palei	PROPN
bibechana-5700	20	4	and	and	CCONJ
bibechana-5700	20	5	n.p	n.p	PROPN
bibechana-5700	20	6	.	.	PROPN
bibechana-5700	20	7	sah	sah	PROPN
bibechana-5700	20	8	/	/	SYM
bibechana-5700	20	9	bibechana	bibechana	PROPN
bibechana-5700	20	10	8	8	NUM
bibechana-5700	20	11	(	(	PUNCT
bibechana-5700	20	12	2012	2012	NUM
bibechana-5700	20	13	)	)	PUNCT
bibechana-5700	20	14	127	127	NUM
bibechana-5700	20	15	-	-	SYM
bibechana-5700	20	16	130	130	NUM
bibechana-5700	20	17	:	:	PUNCT
bibechana-5700	20	18	bmhss	bmhss	PROPN
bibechana-5700	20	19	,	,	PUNCT
bibechana-5700	20	20	p.128	p.128	NOUN
bibechana-5700	20	21	(	(	PUNCT
bibechana-5700	20	22	)	)	PUNCT
bibechana-5700	20	23	(	(	PUNCT
bibechana-5700	20	24	)	)	PUNCT
bibechana-5700	20	25	(	(	PUNCT
bibechana-5700	20	26	)	)	PUNCT
bibechana-5700	20	27	(	(	PUNCT
bibechana-5700	20	28	)	)	PUNCT
bibechana-5700	20	29	,	,	PUNCT
bibechana-5700	21	1	b	b	X
bibechana-5700	21	2	z	z	NOUN
bibechana-5700	21	3	x	x	X
bibechana-5700	21	4	s	s	PROPN
bibechana-5700	21	5	k	k	PROPN
bibechana-5700	21	6	s	s	PROPN
bibechana-5700	21	7	t	t	X
bibechana-5700	21	8	x	x	SYM
bibechana-5700	21	9	t	t	NOUN
bibechana-5700	21	10	dt	dt	X
bibechana-5700	21	11	y	y	PROPN
bibechana-5700	21	12	s−	s−	PROPN
bibechana-5700	22	1	=	=	PRON
bibechana-5700	22	2	∫	∫	PROPN
bibechana-5700	22	3	these	these	DET
bibechana-5700	22	4	equations	equation	NOUN
bibechana-5700	22	5	are	be	AUX
bibechana-5700	22	6	known	know	VERB
bibechana-5700	22	7	as	as	ADP
bibechana-5700	22	8	fredholm	fredholm	ADJ
bibechana-5700	22	9	integral	integral	ADJ
bibechana-5700	22	10	equations	equation	NOUN
bibechana-5700	22	11	.	.	PUNCT
bibechana-5700	23	1	here	here	ADV
bibechana-5700	23	2	k(s	k(s	PROPN
bibechana-5700	23	3	,	,	PUNCT
bibechana-5700	23	4	t	t	PROPN
bibechana-5700	23	5	)	)	PUNCT
bibechana-5700	23	6	is	be	AUX
bibechana-5700	23	7	a	a	DET
bibechana-5700	23	8	continuous	continuous	ADJ
bibechana-5700	23	9	function	function	NOUN
bibechana-5700	23	10	on	on	ADP
bibechana-5700	23	11	[	[	X
bibechana-5700	23	12	a	a	X
bibechana-5700	23	13	,	,	PUNCT
bibechana-5700	23	14	b	b	X
bibechana-5700	23	15	]	]	X
bibechana-5700	23	16	x	x	PUNCT
bibechana-5700	24	1	[	[	X
bibechana-5700	24	2	a	a	X
bibechana-5700	24	3	,	,	PUNCT
bibechana-5700	24	4	b	b	NOUN
bibechana-5700	24	5	]	]	PUNCT
bibechana-5700	24	6	and	and	CCONJ
bibechana-5700	24	7	is	be	AUX
bibechana-5700	24	8	called	call	VERB
bibechana-5700	24	9	the	the	DET
bibechana-5700	24	10	kernel	kernel	NOUN
bibechana-5700	24	11	of	of	ADP
bibechana-5700	24	12	the	the	DET
bibechana-5700	24	13	integral	integral	ADJ
bibechana-5700	24	14	equation	equation	NOUN
bibechana-5700	24	15	,	,	PUNCT
bibechana-5700	24	16	y(s	y(s	PROPN
bibechana-5700	24	17	)	)	PUNCT
bibechana-5700	24	18	is	be	AUX
bibechana-5700	24	19	continuous	continuous	ADJ
bibechana-5700	24	20	on	on	ADP
bibechana-5700	24	21	[	[	X
bibechana-5700	24	22	a	a	X
bibechana-5700	24	23	,	,	PUNCT
bibechana-5700	24	24	b	b	NOUN
bibechana-5700	24	25	]	]	X
bibechana-5700	24	26	,	,	PUNCT
bibechana-5700	24	27	and	and	CCONJ
bibechana-5700	24	28	therefore	therefore	ADV
bibechana-5700	24	29	y∈c[a	y∈c[a	PROPN
bibechana-5700	24	30	,	,	PUNCT
bibechana-5700	24	31	b	b	NOUN
bibechana-5700	24	32	]	]	X
bibechana-5700	24	33	.	.	PUNCT
bibechana-5700	25	1	as	as	SCONJ
bibechana-5700	25	2	solutions	solution	NOUN
bibechana-5700	25	3	only	only	ADV
bibechana-5700	25	4	elements	element	NOUN
bibechana-5700	25	5	from	from	ADP
bibechana-5700	25	6	c[a	c[a	NUM
bibechana-5700	25	7	,	,	PUNCT
bibechana-5700	25	8	b	b	AUX
bibechana-5700	25	9	]	]	PUNCT
bibechana-5700	25	10	are	be	AUX
bibechana-5700	25	11	allowed	allow	VERB
bibechana-5700	25	12	.	.	PUNCT
bibechana-5700	26	1	therefore	therefore	ADV
bibechana-5700	26	2	we	we	PRON
bibechana-5700	26	3	can	can	AUX
bibechana-5700	26	4	write	write	VERB
bibechana-5700	26	5	the	the	DET
bibechana-5700	26	6	integral	integral	ADJ
bibechana-5700	26	7	equation	equation	NOUN
bibechana-5700	26	8	also	also	ADV
bibechana-5700	26	9	in	in	ADP
bibechana-5700	26	10	the	the	DET
bibechana-5700	26	11	following	follow	VERB
bibechana-5700	26	12	abstract	abstract	ADJ
bibechana-5700	26	13	form	form	NOUN
bibechana-5700	26	14	.	.	PUNCT
bibechana-5700	27	1	(	(	PUNCT
bibechana-5700	27	2	)	)	PUNCT
bibechana-5700	27	3	x	x	X
bibechana-5700	27	4	kx	kx	PROPN
bibechana-5700	28	1	i	i	PRON
bibechana-5700	28	2	k	k	NOUN
bibechana-5700	28	3	x	x	PUNCT
bibechana-5700	28	4	y−	y−	X
bibechana-5700	28	5	=	=	PUNCT
bibechana-5700	28	6	−	−	PROPN
bibechana-5700	29	1	=	=	SYM
bibechana-5700	29	2	,	,	PUNCT
bibechana-5700	29	3	where	where	SCONJ
bibechana-5700	29	4	i	i	PRON
bibechana-5700	29	5	is	be	AUX
bibechana-5700	29	6	the	the	DET
bibechana-5700	29	7	identity	identity	NOUN
bibechana-5700	29	8	map	map	NOUN
bibechana-5700	29	9	on	on	ADP
bibechana-5700	29	10	c[a	c[a	NUM
bibechana-5700	29	11	,	,	PUNCT
bibechana-5700	29	12	b	b	NOUN
bibechana-5700	29	13	]	]	PUNCT
bibechana-5700	29	14	and	and	CCONJ
bibechana-5700	29	15	where	where	SCONJ
bibechana-5700	29	16	the	the	DET
bibechana-5700	29	17	linear	linear	PROPN
bibechana-5700	29	18	map	map	NOUN
bibechana-5700	29	19	k	k	X
bibechana-5700	29	20	:	:	PUNCT
bibechana-5700	29	21	c[a	c[a	NUM
bibechana-5700	29	22	,	,	PUNCT
bibechana-5700	29	23	b]→c[a	b]→c[a	PROPN
bibechana-5700	29	24	,	,	PUNCT
bibechana-5700	29	25	b	b	AUX
bibechana-5700	29	26	]	]	PUNCT
bibechana-5700	29	27	is	be	AUX
bibechana-5700	29	28	defined	define	VERB
bibechana-5700	29	29	by	by	ADP
bibechana-5700	29	30	(	(	PUNCT
bibechana-5700	29	31	)	)	PUNCT
bibechana-5700	29	32	(	(	PUNCT
bibechana-5700	29	33	)	)	PUNCT
bibechana-5700	29	34	(	(	PUNCT
bibechana-5700	29	35	)	)	PUNCT
bibechana-5700	29	36	(	(	PUNCT
bibechana-5700	29	37	)	)	PUNCT
bibechana-5700	29	38	,	,	PUNCT
bibechana-5700	29	39	b	b	PROPN
bibechana-5700	29	40	a	a	PRON
bibechana-5700	30	1	kx	kx	PROPN
bibechana-5700	30	2	s	s	PROPN
bibechana-5700	31	1	k	k	PROPN
bibechana-5700	31	2	s	s	PROPN
bibechana-5700	31	3	t	t	X
bibechana-5700	31	4	x	x	SYM
bibechana-5700	31	5	t	t	PROPN
bibechana-5700	31	6	dt=	dt=	PROPN
bibechana-5700	31	7	∫	∫	PROPN
bibechana-5700	31	8	.	.	PUNCT
bibechana-5700	32	1	further	far	ADV
bibechana-5700	32	2	,	,	PUNCT
bibechana-5700	32	3	if	if	SCONJ
bibechana-5700	32	4	in	in	ADP
bibechana-5700	32	5	fredholm	fredholm	NOUN
bibechana-5700	32	6	aternative	aternative	ADJ
bibechana-5700	32	7	theorem	theorem	NOUN
bibechana-5700	32	8	we	we	PRON
bibechana-5700	32	9	replace	replace	VERB
bibechana-5700	32	10	t	t	NOUN
bibechana-5700	32	11	by	by	ADP
bibechana-5700	32	12	i	i	PROPN
bibechana-5700	32	13	-	-	PUNCT
bibechana-5700	32	14	k	k	PROPN
bibechana-5700	32	15	then	then	ADV
bibechana-5700	32	16	in	in	ADP
bibechana-5700	32	17	that	that	DET
bibechana-5700	32	18	case	case	NOUN
bibechana-5700	32	19	it	it	PRON
bibechana-5700	32	20	reads[7	reads[7	AUX
bibechana-5700	32	21	]	]	PUNCT
bibechana-5700	32	22	:	:	PUNCT
bibechana-5700	32	23	either	either	CCONJ
bibechana-5700	32	24	the	the	DET
bibechana-5700	32	25	equation	equation	NOUN
bibechana-5700	32	26	(	(	PUNCT
bibechana-5700	32	27	i	i	PROPN
bibechana-5700	32	28	-	-	PUNCT
bibechana-5700	32	29	k)x=0	k)x=0	PROPN
bibechana-5700	32	30	has	have	VERB
bibechana-5700	32	31	only	only	ADV
bibechana-5700	32	32	the	the	DET
bibechana-5700	32	33	trivial	trivial	ADJ
bibechana-5700	32	34	solution	solution	NOUN
bibechana-5700	32	35	x	x	PUNCT
bibechana-5700	33	1	=	=	SYM
bibechana-5700	33	2	0	0	NUM
bibechana-5700	33	3	in	in	ADP
bibechana-5700	33	4	which	which	DET
bibechana-5700	33	5	case	case	NOUN
bibechana-5700	33	6	the	the	DET
bibechana-5700	33	7	equation	equation	NOUN
bibechana-5700	33	8	(	(	PUNCT
bibechana-5700	33	9	i	i	NOUN
bibechana-5700	33	10	-	-	PUNCT
bibechana-5700	33	11	k)x	k)x	X
bibechana-5700	33	12	=	=	NOUN
bibechana-5700	33	13	y	y	PROPN
bibechana-5700	33	14	has	have	VERB
bibechana-5700	33	15	a	a	DET
bibechana-5700	33	16	unique	unique	ADJ
bibechana-5700	33	17	solution	solution	NOUN
bibechana-5700	33	18	x∈c[a	x∈c[a	PROPN
bibechana-5700	33	19	,	,	PUNCT
bibechana-5700	33	20	b	b	X
bibechana-5700	33	21	]	]	X
bibechana-5700	33	22	for	for	ADP
bibechana-5700	33	23	arbitrary	arbitrary	ADJ
bibechana-5700	33	24	y∈c[a	y∈c[a	NOUN
bibechana-5700	33	25	,	,	PUNCT
bibechana-5700	33	26	b	b	NOUN
bibechana-5700	33	27	]	]	X
bibechana-5700	33	28	.	.	PUNCT
bibechana-5700	34	1	or	or	CCONJ
bibechana-5700	34	2	the	the	DET
bibechana-5700	34	3	equation	equation	NOUN
bibechana-5700	34	4	(	(	PUNCT
bibechana-5700	34	5	i	i	NOUN
bibechana-5700	34	6	-	-	PUNCT
bibechana-5700	34	7	k)x	k)x	ADJ
bibechana-5700	34	8	=	=	SYM
bibechana-5700	34	9	0	0	NUM
bibechana-5700	34	10	has	have	VERB
bibechana-5700	34	11	non	non	ADJ
bibechana-5700	34	12	-	-	ADJ
bibechana-5700	34	13	trivial	trivial	ADJ
bibechana-5700	34	14	solution	solution	NOUN
bibechana-5700	34	15	in	in	ADP
bibechana-5700	34	16	c[a	c[a	NUM
bibechana-5700	34	17	,	,	PUNCT
bibechana-5700	34	18	b	b	X
bibechana-5700	34	19	]	]	PUNCT
bibechana-5700	34	20	in	in	ADP
bibechana-5700	34	21	which	which	DET
bibechana-5700	34	22	case	case	NOUN
bibechana-5700	34	23	the	the	DET
bibechana-5700	34	24	equation	equation	NOUN
bibechana-5700	34	25	(	(	PUNCT
bibechana-5700	34	26	i	i	NOUN
bibechana-5700	34	27	-	-	PUNCT
bibechana-5700	34	28	k)x	k)x	ADV
bibechana-5700	34	29	=	=	PUNCT
bibechana-5700	34	30	y	y	NOUN
bibechana-5700	34	31	is	be	AUX
bibechana-5700	34	32	not	not	PART
bibechana-5700	34	33	necessarily	necessarily	ADV
bibechana-5700	34	34	solvable	solvable	ADJ
bibechana-5700	34	35	through	through	ADP
bibechana-5700	34	36	an	an	DET
bibechana-5700	34	37	x∈c[a	x∈c[a	PROPN
bibechana-5700	34	38	,	,	PUNCT
bibechana-5700	34	39	b	b	X
bibechana-5700	34	40	]	]	X
bibechana-5700	34	41	for	for	ADP
bibechana-5700	34	42	arbitrary	arbitrary	ADJ
bibechana-5700	34	43	y∈c[a	y∈c[a	NOUN
bibechana-5700	34	44	,	,	PUNCT
bibechana-5700	34	45	b	b	NOUN
bibechana-5700	34	46	]	]	PUNCT
bibechana-5700	34	47	.	.	PUNCT
bibechana-5700	35	1	in	in	ADP
bibechana-5700	35	2	order	order	NOUN
bibechana-5700	35	3	to	to	PART
bibechana-5700	35	4	give	give	VERB
bibechana-5700	35	5	a	a	DET
bibechana-5700	35	6	refinement	refinement	NOUN
bibechana-5700	35	7	of	of	ADP
bibechana-5700	35	8	fredholm	fredholm	NOUN
bibechana-5700	35	9	alternative	alternative	ADJ
bibechana-5700	35	10	theorem	theorem	NOUN
bibechana-5700	35	11	we	we	PRON
bibechana-5700	35	12	introduce	introduce	VERB
bibechana-5700	35	13	the	the	DET
bibechana-5700	35	14	following	following	ADJ
bibechana-5700	35	15	definitions	definition	NOUN
bibechana-5700	35	16	:	:	PUNCT
bibechana-5700	35	17	1	1	X
bibechana-5700	35	18	.	.	X
bibechana-5700	35	19	definition	definition	NOUN
bibechana-5700	35	20	k∈l(x	k∈l(x	PROPN
bibechana-5700	35	21	)	)	PUNCT
bibechana-5700	35	22	is	be	AUX
bibechana-5700	35	23	called	call	VERB
bibechana-5700	35	24	finite	finite	ADJ
bibechana-5700	35	25	dimensional	dimensional	ADJ
bibechana-5700	35	26	or	or	CCONJ
bibechana-5700	35	27	of	of	ADP
bibechana-5700	35	28	finite	finite	ADJ
bibechana-5700	35	29	rank	rank	NOUN
bibechana-5700	35	30	of	of	ADP
bibechana-5700	35	31	dim	dim	ADJ
bibechana-5700	35	32	b(k)<∞.	b(k)<∞.	NOUN
bibechana-5700	35	33	let	let	VERB
bibechana-5700	35	34	x	x	PRON
bibechana-5700	35	35	,	,	PUNCT
bibechana-5700	35	36	y	y	PROPN
bibechana-5700	35	37	be	be	VERB
bibechana-5700	35	38	vector	vector	NOUN
bibechana-5700	35	39	spaces	space	NOUN
bibechana-5700	35	40	over	over	ADP
bibechana-5700	35	41	the	the	DET
bibechana-5700	35	42	same	same	ADJ
bibechana-5700	35	43	field	field	NOUN
bibechana-5700	35	44	of	of	ADP
bibechana-5700	35	45	scalars	scalar	NOUN
bibechana-5700	35	46	and	and	CCONJ
bibechana-5700	35	47	let	let	VERB
bibechana-5700	35	48	l(x	l(x	PROPN
bibechana-5700	35	49	,	,	PUNCT
bibechana-5700	35	50	y	y	PROPN
bibechana-5700	35	51	)	)	PUNCT
bibechana-5700	35	52	denote	denote	VERB
bibechana-5700	35	53	the	the	DET
bibechana-5700	35	54	vector	vector	NOUN
bibechana-5700	35	55	space	space	NOUN
bibechana-5700	35	56	of	of	ADP
bibechana-5700	35	57	all	all	DET
bibechana-5700	35	58	linear	linear	ADJ
bibechana-5700	35	59	mappings	mapping	NOUN
bibechana-5700	35	60	of	of	ADP
bibechana-5700	35	61	x	x	PUNCT
bibechana-5700	35	62	into	into	ADP
bibechana-5700	35	63	y.	y.	NOUN
bibechana-5700	35	64	let	let	VERB
bibechana-5700	35	65	t∈l(x	t∈l(x	PROPN
bibechana-5700	35	66	,	,	PUNCT
bibechana-5700	35	67	y	y	PROPN
bibechana-5700	35	68	)	)	PUNCT
bibechana-5700	35	69	.	.	PUNCT
bibechana-5700	36	1	then	then	ADV
bibechana-5700	36	2	α(t	α(t	VERB
bibechana-5700	36	3	)	)	PUNCT
bibechana-5700	37	1	=	=	SYM
bibechana-5700	37	2	dimn(t	dimn(t	PROPN
bibechana-5700	37	3	)	)	PUNCT
bibechana-5700	37	4	is	be	AUX
bibechana-5700	37	5	called	call	VERB
bibechana-5700	37	6	the	the	DET
bibechana-5700	37	7	kernel	kernel	PROPN
bibechana-5700	37	8	index	index	NOUN
bibechana-5700	37	9	of	of	ADP
bibechana-5700	37	10	t([1][.2	t([1][.2	PROPN
bibechana-5700	37	11	]	]	PUNCT
bibechana-5700	37	12	)	)	PUNCT
bibechana-5700	37	13	.	.	PUNCT
bibechana-5700	38	1	β(t	β(t	PROPN
bibechana-5700	38	2	)	)	PUNCT
bibechana-5700	39	1	=	=	PRON
bibechana-5700	39	2	co	co	NOUN
bibechana-5700	39	3	-	-	NOUN
bibechana-5700	39	4	dimb(t	dimb(t	NOUN
bibechana-5700	39	5	)	)	PUNCT
bibechana-5700	39	6	=	=	VERB
bibechana-5700	40	1	dim	dim	ADJ
bibechana-5700	40	2	y	y	PROPN
bibechana-5700	40	3	/	/	SYM
bibechana-5700	40	4	b(t	b(t	NOUN
bibechana-5700	40	5	)	)	PUNCT
bibechana-5700	40	6	is	be	AUX
bibechana-5700	40	7	called	call	VERB
bibechana-5700	40	8	the	the	DET
bibechana-5700	40	9	deficiency	deficiency	NOUN
bibechana-5700	40	10	index	index	NOUN
bibechana-5700	40	11	of	of	ADP
bibechana-5700	40	12	t.	t.	PROPN
bibechana-5700	40	13	the	the	DET
bibechana-5700	40	14	following	follow	VERB
bibechana-5700	40	15	theorem	theorem	NOUN
bibechana-5700	40	16	is	be	AUX
bibechana-5700	40	17	a	a	DET
bibechana-5700	40	18	refinement	refinement	NOUN
bibechana-5700	40	19	of	of	ADP
bibechana-5700	40	20	fredholm	fredholm	NOUN
bibechana-5700	40	21	alternative	alternative	NOUN
bibechana-5700	40	22	theorem	theorem	NOUN
bibechana-5700	40	23	:	:	PUNCT
bibechana-5700	40	24	theorem	theorem	ADJ
bibechana-5700	40	25	:	:	PUNCT
bibechana-5700	40	26	if	if	SCONJ
bibechana-5700	40	27	k	k	PROPN
bibechana-5700	40	28	is	be	AUX
bibechana-5700	40	29	a	a	DET
bibechana-5700	40	30	finite	finite	ADJ
bibechana-5700	40	31	dimensional	dimensional	ADJ
bibechana-5700	40	32	map	map	NOUN
bibechana-5700	40	33	of	of	ADP
bibechana-5700	40	34	x	x	PUNCT
bibechana-5700	40	35	into	into	ADP
bibechana-5700	40	36	itself	itself	PRON
bibechana-5700	40	37	then	then	ADV
bibechana-5700	40	38	α(i	α(i	PROPN
bibechana-5700	40	39	-	-	PUNCT
bibechana-5700	40	40	k)=	k)=	VERB
bibechana-5700	40	41	β(i	β(i	NOUN
bibechana-5700	40	42	-	-	PUNCT
bibechana-5700	40	43	k)<∞.	k)<∞.	NOUN
bibechana-5700	40	44	proof	proof	NOUN
bibechana-5700	40	45	:	:	PUNCT
bibechana-5700	40	46	(	(	PUNCT
bibechana-5700	40	47	a	a	X
bibechana-5700	40	48	)	)	PUNCT
bibechana-5700	40	49	we	we	PRON
bibechana-5700	40	50	first	first	ADV
bibechana-5700	40	51	show	show	VERB
bibechana-5700	40	52	that	that	SCONJ
bibechana-5700	40	53	α	α	PRON
bibechana-5700	40	54	(	(	PUNCT
bibechana-5700	40	55	i	i	PROPN
bibechana-5700	40	56	-	-	PUNCT
bibechana-5700	40	57	k	k	NOUN
bibechana-5700	40	58	)	)	PUNCT
bibechana-5700	40	59	≤	≤	NUM
bibechana-5700	40	60	dimb(k	dimb(k	NOUN
bibechana-5700	40	61	)	)	PUNCT
bibechana-5700	40	62	,	,	PUNCT
bibechana-5700	40	63	in	in	ADP
bibechana-5700	40	64	fact	fact	NOUN
bibechana-5700	40	65	if	if	SCONJ
bibechana-5700	40	66	x∈n(i	x∈n(i	PROPN
bibechana-5700	40	67	-	-	PUNCT
bibechana-5700	40	68	k	k	NOUN
bibechana-5700	40	69	)	)	PUNCT
bibechana-5700	40	70	then	then	ADV
bibechana-5700	40	71	x	x	X
bibechana-5700	40	72	=	=	SYM
bibechana-5700	40	73	kx	kx	PROPN
bibechana-5700	40	74	,	,	PUNCT
bibechana-5700	40	75	hence	hence	ADV
bibechana-5700	40	76	n(i	n(i	PROPN
bibechana-5700	40	77	-	-	PUNCT
bibechana-5700	40	78	k)⊆b(k	k)⊆b(k	NOUN
bibechana-5700	40	79	)	)	PUNCT
bibechana-5700	40	80	and	and	CCONJ
bibechana-5700	40	81	α	α	PROPN
bibechana-5700	40	82	(	(	PUNCT
bibechana-5700	40	83	i	i	NOUN
bibechana-5700	40	84	-	-	PUNCT
bibechana-5700	40	85	k)≤dimb(k	k)≤dimb(k	PROPN
bibechana-5700	40	86	)	)	PUNCT
bibechana-5700	40	87	.	.	PUNCT
bibechana-5700	41	1	(	(	PUNCT
bibechana-5700	41	2	b	b	X
bibechana-5700	41	3	)	)	PUNCT
bibechana-5700	41	4	we	we	PRON
bibechana-5700	41	5	put	put	VERB
bibechana-5700	41	6	y	y	PROPN
bibechana-5700	41	7	=	=	SYM
bibechana-5700	41	8	b(k	b(k	PROPN
bibechana-5700	41	9	)	)	PUNCT
bibechana-5700	41	10	.	.	PUNCT
bibechana-5700	42	1	since	since	SCONJ
bibechana-5700	42	2	b(k	b(k	PROPN
bibechana-5700	42	3	2	2	NUM
bibechana-5700	42	4	)	)	PUNCT
bibechana-5700	42	5	⊆b(k	⊆b(k	NOUN
bibechana-5700	42	6	)	)	PUNCT
bibechana-5700	42	7	,	,	PUNCT
bibechana-5700	42	8	k	k	PROPN
bibechana-5700	42	9	and	and	CCONJ
bibechana-5700	42	10	hence	hence	ADV
bibechana-5700	42	11	also	also	ADV
bibechana-5700	42	12	i	i	PROPN
bibechana-5700	42	13	-	-	PUNCT
bibechana-5700	42	14	k	k	PROPN
bibechana-5700	42	15	map	map	NOUN
bibechana-5700	42	16	y	y	PROPN
bibechana-5700	42	17	into	into	ADP
bibechana-5700	42	18	itself	itself	PRON
bibechana-5700	42	19	.	.	PUNCT
bibechana-5700	43	1	we	we	PRON
bibechana-5700	43	2	denote	denote	VERB
bibechana-5700	43	3	the	the	DET
bibechana-5700	43	4	restrictions	restriction	NOUN
bibechana-5700	43	5	of	of	ADP
bibechana-5700	43	6	i	i	PRON
bibechana-5700	43	7	,	,	PUNCT
bibechana-5700	43	8	k	k	PROPN
bibechana-5700	43	9	to	to	ADP
bibechana-5700	43	10	y	y	PROPN
bibechana-5700	43	11	by	by	ADP
bibechana-5700	43	12	�	�	PROPN
bibechana-5700	43	13	,	,	PUNCT
bibechana-5700	43	14	i	i	PRON
bibechana-5700	43	15	kɶ	kɶ	VERB
bibechana-5700	43	16	.	.	PUNCT
bibechana-5700	44	1	by	by	ADP
bibechana-5700	44	2	(	(	PUNCT
bibechana-5700	44	3	a	a	X
bibechana-5700	44	4	)	)	PUNCT
bibechana-5700	44	5	we	we	PRON
bibechana-5700	44	6	have	have	AUX
bibechana-5700	44	7	�	�	NOUN
bibechana-5700	44	8	(	(	PUNCT
bibechana-5700	44	9	)	)	PUNCT
bibechana-5700	44	10	(	(	PUNCT
bibechana-5700	44	11	)	)	PUNCT
bibechana-5700	44	12	i	i	PRON
bibechana-5700	44	13	k	k	PROPN
bibechana-5700	45	1	n	n	VERB
bibechana-5700	46	1	i	i	PRON
bibechana-5700	46	2	k−	k−	PROPN
bibechana-5700	46	3	=	=	PUNCT
bibechana-5700	47	1	−ɶ	−ɶ	INTJ
bibechana-5700	47	2	,	,	PUNCT
bibechana-5700	47	3	if	if	SCONJ
bibechana-5700	47	4	z	z	NOUN
bibechana-5700	47	5	is	be	AUX
bibechana-5700	47	6	an	an	DET
bibechana-5700	47	7	algebric	algebric	ADJ
bibechana-5700	47	8	components	component	NOUN
bibechana-5700	47	9	space	space	NOUN
bibechana-5700	47	10	of	of	ADP
bibechana-5700	47	11	�	�	PROPN
bibechana-5700	47	12	(	(	PUNCT
bibechana-5700	47	13	)	)	PUNCT
bibechana-5700	47	14	b	b	NOUN
bibechana-5700	48	1	i	i	PRON
bibechana-5700	48	2	k−ɶ	k−ɶ	PROPN
bibechana-5700	48	3	in	in	ADP
bibechana-5700	48	4	y	y	PROPN
bibechana-5700	48	5	then	then	ADV
bibechana-5700	48	6	z	z	PROPN
bibechana-5700	48	7	has	have	VERB
bibechana-5700	48	8	finite	finite	ADJ
bibechana-5700	48	9	dimension	dimension	NOUN
bibechana-5700	48	10	since	since	SCONJ
bibechana-5700	48	11	dim	dim	ADJ
bibechana-5700	48	12	y<∞.	y<∞.	PROPN
bibechana-5700	48	13	now	now	ADV
bibechana-5700	48	14	,	,	PUNCT
bibechana-5700	48	15	since	since	SCONJ
bibechana-5700	48	16	�	�	PROPN
bibechana-5700	48	17	i	i	PRON
bibechana-5700	48	18	k−ɶ	k−ɶ	PROPN
bibechana-5700	48	19	is	be	AUX
bibechana-5700	48	20	a	a	DET
bibechana-5700	48	21	map	map	NOUN
bibechana-5700	48	22	of	of	ADP
bibechana-5700	48	23	a	a	DET
bibechana-5700	48	24	finite	finite	ADJ
bibechana-5700	48	25	dimensional	dimensional	ADJ
bibechana-5700	48	26	space	space	NOUN
bibechana-5700	48	27	into	into	ADP
bibechana-5700	48	28	itself	itself	PRON
bibechana-5700	48	29	,	,	PUNCT
bibechana-5700	48	30	we	we	PRON
bibechana-5700	48	31	have	have	VERB
bibechana-5700	48	32	α	α	DET
bibechana-5700	48	33	�	�	PROPN
bibechana-5700	48	34	(	(	PUNCT
bibechana-5700	48	35	)	)	PUNCT
bibechana-5700	48	36	�	�	PROPN
bibechana-5700	48	37	(	(	PUNCT
bibechana-5700	48	38	)	)	PUNCT
bibechana-5700	49	1	i	i	PRON
bibechana-5700	49	2	k	k	NOUN
bibechana-5700	50	1	i	i	PRON
bibechana-5700	50	2	kβ−	kβ−	PUNCT
bibechana-5700	50	3	=	=	X
bibechana-5700	50	4	−ɶ	−ɶ	PROPN
bibechana-5700	50	5	ɶ	ɶ	NOUN
bibechana-5700	50	6	and	and	CCONJ
bibechana-5700	50	7	hence	hence	ADV
bibechana-5700	50	8	α	α	PROPN
bibechana-5700	50	9	(	(	PUNCT
bibechana-5700	50	10	)	)	PUNCT
bibechana-5700	50	11	dimi	dimi	PROPN
bibechana-5700	50	12	k	k	PROPN
bibechana-5700	50	13	z−	z−	PROPN
bibechana-5700	50	14	=	=	PUNCT
bibechana-5700	50	15	.	.	PUNCT
bibechana-5700	51	1	(	(	PUNCT
bibechana-5700	51	2	c	c	X
bibechana-5700	51	3	)	)	PUNCT
bibechana-5700	51	4	we	we	PRON
bibechana-5700	51	5	show	show	VERB
bibechana-5700	51	6	that	that	SCONJ
bibechana-5700	51	7	dinz	dinz	PROPN
bibechana-5700	51	8	=	=	PROPN
bibechana-5700	51	9	b(i	b(i	PROPN
bibechana-5700	51	10	-	-	NOUN
bibechana-5700	51	11	k	k	NOUN
bibechana-5700	51	12	)	)	PUNCT
bibechana-5700	51	13	,	,	PUNCT
bibechana-5700	51	14	from	from	ADP
bibechana-5700	51	15	which	which	PRON
bibechana-5700	51	16	the	the	DET
bibechana-5700	51	17	result	result	NOUN
bibechana-5700	51	18	follows	follow	VERB
bibechana-5700	51	19	due	due	ADJ
bibechana-5700	51	20	to	to	ADP
bibechana-5700	51	21	(	(	PUNCT
bibechana-5700	51	22	b	b	NOUN
bibechana-5700	51	23	)	)	PUNCT
bibechana-5700	51	24	,	,	PUNCT
bibechana-5700	51	25	for	for	ADP
bibechana-5700	51	26	this	this	DET
bibechana-5700	51	27	purpose	purpose	NOUN
bibechana-5700	51	28	we	we	PRON
bibechana-5700	51	29	prove	prove	VERB
bibechana-5700	51	30	that	that	SCONJ
bibechana-5700	51	31	x	x	X
bibechana-5700	51	32	=	=	PUNCT
bibechana-5700	51	33	z⊕b(i	z⊕b(i	NOUN
bibechana-5700	51	34	-	-	NOUN
bibechana-5700	51	35	k	k	NOUN
bibechana-5700	51	36	)	)	PUNCT
bibechana-5700	51	37	or	or	CCONJ
bibechana-5700	51	38	equivalent	equivalent	ADJ
bibechana-5700	51	39	that	that	SCONJ
bibechana-5700	51	40	x	x	X
bibechana-5700	51	41	=	=	SYM
bibechana-5700	51	42	z+b(i	z+b(i	NUM
bibechana-5700	51	43	-	-	NOUN
bibechana-5700	51	44	k	k	NOUN
bibechana-5700	51	45	)	)	PUNCT
bibechana-5700	51	46	and	and	CCONJ
bibechana-5700	51	47	{	{	PUNCT
bibechana-5700	51	48	0}=z∩b(i	0}=z∩b(i	NOUN
bibechana-5700	51	49	-	-	PUNCT
bibechana-5700	51	50	k	k	NOUN
bibechana-5700	51	51	)	)	PUNCT
bibechana-5700	51	52	.	.	PUNCT
bibechana-5700	52	1	if	if	SCONJ
bibechana-5700	52	2	y	y	PROPN
bibechana-5700	52	3	=	=	PRON
bibechana-5700	52	4	(	(	PUNCT
bibechana-5700	52	5	i	i	NOUN
bibechana-5700	52	6	-	-	PUNCT
bibechana-5700	52	7	k)x	k)x	ADJ
bibechana-5700	52	8	,	,	PUNCT
bibechana-5700	52	9	x∈x	x∈x	PROPN
bibechana-5700	52	10	,	,	PUNCT
bibechana-5700	52	11	then	then	ADV
bibechana-5700	52	12	for	for	ADP
bibechana-5700	52	13	suitable	suitable	ADJ
bibechana-5700	52	14	g∈g	g∈g	NOUN
bibechana-5700	52	15	,	,	PUNCT
bibechana-5700	52	16	z∈y	z∈y	NUM
bibechana-5700	52	17	we	we	PRON
bibechana-5700	52	18	have	have	VERB
bibechana-5700	52	19	x	x	X
bibechana-5700	52	20	=	=	PUNCT
bibechana-5700	52	21	y	y	PROPN
bibechana-5700	52	22	+	+	CCONJ
bibechana-5700	52	23	kx	kx	PROPN
bibechana-5700	52	24	=	=	SYM
bibechana-5700	52	25	y	y	PROPN
bibechana-5700	53	1	+	+	CCONJ
bibechana-5700	53	2	(	(	PUNCT
bibechana-5700	53	3	g	g	PROPN
bibechana-5700	53	4	+	+	CCONJ
bibechana-5700	53	5	(	(	PUNCT
bibechana-5700	53	6	i	i	NOUN
bibechana-5700	53	7	-	-	PUNCT
bibechana-5700	53	8	k)z	k)z	PROPN
bibechana-5700	53	9	)	)	PUNCT
bibechana-5700	53	10	=	=	SYM
bibechana-5700	54	1	g	g	PROPN
bibechana-5700	54	2	+	+	CCONJ
bibechana-5700	54	3	(	(	PUNCT
bibechana-5700	54	4	i	i	NOUN
bibechana-5700	54	5	-	-	PUNCT
bibechana-5700	54	6	k)(x+z	k)(x+z	VERB
bibechana-5700	54	7	)	)	PUNCT
bibechana-5700	54	8	,	,	PUNCT
bibechana-5700	54	9	therefore	therefore	ADV
bibechana-5700	54	10	x	x	X
bibechana-5700	54	11	=	=	SYM
bibechana-5700	54	12	g+b(i	g+b(i	NOUN
bibechana-5700	54	13	-	-	NOUN
bibechana-5700	54	14	k	k	NOUN
bibechana-5700	54	15	)	)	PUNCT
bibechana-5700	54	16	.	.	PUNCT
bibechana-5700	55	1	if	if	SCONJ
bibechana-5700	55	2	u∈z∩b(i	u∈z∩b(i	PROPN
bibechana-5700	55	3	-	-	PROPN
bibechana-5700	55	4	k	k	NOUN
bibechana-5700	55	5	)	)	PUNCT
bibechana-5700	55	6	then	then	ADV
bibechana-5700	55	7	u	u	X
bibechana-5700	55	8	=	=	PUNCT
bibechana-5700	55	9	(	(	PUNCT
bibechana-5700	55	10	i	i	PROPN
bibechana-5700	55	11	-	-	PUNCT
bibechana-5700	55	12	k)v∈z	k)v∈z	PROPN
bibechana-5700	55	13	.	.	PUNCT
bibechana-5700	56	1	then	then	ADV
bibechana-5700	56	2	v	v	X
bibechana-5700	56	3	=	=	SYM
bibechana-5700	56	4	u	u	NOUN
bibechana-5700	56	5	+	+	X
bibechana-5700	56	6	kv∈y	kv∈y	NOUN
bibechana-5700	56	7	,	,	PUNCT
bibechana-5700	56	8	therefore	therefore	ADV
bibechana-5700	56	9	u	u	X
bibechana-5700	56	10	=	=	PUNCT
bibechana-5700	56	11	(	(	PUNCT
bibechana-5700	56	12	i	i	PROPN
bibechana-5700	56	13	-	-	PUNCT
bibechana-5700	56	14	k	k	NOUN
bibechana-5700	56	15	)	)	PUNCT
bibechana-5700	56	16	v∈b(i	v∈b(i	NOUN
bibechana-5700	56	17	-	-	PUNCT
bibechana-5700	56	18	k)∩z	k)∩z	PROPN
bibechana-5700	56	19	=	=	PUNCT
bibechana-5700	56	20	{	{	PUNCT
bibechana-5700	56	21	0	0	NUM
bibechana-5700	56	22	}	}	PUNCT
bibechana-5700	56	23	.	.	PUNCT
bibechana-5700	57	1	this	this	PRON
bibechana-5700	57	2	complete	complete	VERB
bibechana-5700	57	3	the	the	DET
bibechana-5700	57	4	proof	proof	NOUN
bibechana-5700	57	5	.	.	PUNCT
bibechana-5700	58	1	illustration	illustration	NOUN
bibechana-5700	58	2	:	:	PUNCT
bibechana-5700	58	3	the	the	DET
bibechana-5700	58	4	vector	vector	NOUN
bibechana-5700	58	5	space	space	NOUN
bibechana-5700	58	6	c[a	c[a	NOUN
bibechana-5700	58	7	,	,	PUNCT
bibechana-5700	58	8	b	b	NOUN
bibechana-5700	58	9	]	]	PUNCT
bibechana-5700	58	10	becomes	become	VERB
bibechana-5700	58	11	a	a	DET
bibechana-5700	58	12	banach	banach	NOUN
bibechana-5700	58	13	space	space	NOUN
bibechana-5700	58	14	if	if	SCONJ
bibechana-5700	58	15	we	we	PRON
bibechana-5700	58	16	define	define	VERB
bibechana-5700	58	17	||x||	||x||	ADV
bibechana-5700	58	18	=	=	SYM
bibechana-5700	58	19	sup	sup	NOUN
bibechana-5700	58	20	|x(t)|	|x(t)|	PROPN
bibechana-5700	58	21	for	for	ADP
bibechana-5700	58	22	all	all	DET
bibechana-5700	58	23	t∈[a	t∈[a	NOUN
bibechana-5700	58	24	,	,	PUNCT
bibechana-5700	58	25	b	b	NOUN
bibechana-5700	58	26	]	]	X
bibechana-5700	58	27	.	.	PUNCT
bibechana-5700	59	1	as	as	ADP
bibechana-5700	59	2	k(s	k(s	PROPN
bibechana-5700	59	3	,	,	PUNCT
bibechana-5700	59	4	t	t	PROPN
bibechana-5700	59	5	)	)	PUNCT
bibechana-5700	59	6	is	be	AUX
bibechana-5700	59	7	continuous	continuous	ADJ
bibechana-5700	59	8	on	on	ADP
bibechana-5700	59	9	the	the	DET
bibechana-5700	59	10	closed	closed	ADJ
bibechana-5700	59	11	rectangle	rectangle	NOUN
bibechana-5700	59	12	[	[	X
bibechana-5700	59	13	a	a	X
bibechana-5700	59	14	,	,	PUNCT
bibechana-5700	59	15	b	b	X
bibechana-5700	59	16	]	]	X
bibechana-5700	59	17	x	x	PUNCT
bibechana-5700	60	1	[	[	X
bibechana-5700	60	2	a	a	X
bibechana-5700	60	3	,	,	PUNCT
bibechana-5700	60	4	b	b	NOUN
bibechana-5700	60	5	]	]	X
bibechana-5700	60	6	g.k	g.k	PROPN
bibechana-5700	60	7	.	.	PROPN
bibechana-5700	60	8	palei	palei	PROPN
bibechana-5700	60	9	and	and	CCONJ
bibechana-5700	60	10	n.p	n.p	PROPN
bibechana-5700	60	11	.	.	PROPN
bibechana-5700	60	12	sah	sah	PROPN
bibechana-5700	60	13	/	/	SYM
bibechana-5700	60	14	bibechana	bibechana	PROPN
bibechana-5700	60	15	8	8	NUM
bibechana-5700	60	16	(	(	PUNCT
bibechana-5700	60	17	2012	2012	NUM
bibechana-5700	60	18	)	)	PUNCT
bibechana-5700	60	19	127	127	NUM
bibechana-5700	60	20	-	-	SYM
bibechana-5700	60	21	130	130	NUM
bibechana-5700	60	22	:	:	PUNCT
bibechana-5700	60	23	bmhss	bmhss	PROPN
bibechana-5700	60	24	,	,	PUNCT
bibechana-5700	60	25	p.129	p.129	PROPN
bibechana-5700	60	26	we	we	PRON
bibechana-5700	60	27	have	have	VERB
bibechana-5700	60	28	|k(s	|k(s	PROPN
bibechana-5700	60	29	,	,	PUNCT
bibechana-5700	60	30	t)|	t)|	ADJ
bibechana-5700	60	31	≤	≤	NUM
bibechana-5700	60	32	µ	µ	NOUN
bibechana-5700	60	33	for	for	ADP
bibechana-5700	60	34	all	all	DET
bibechana-5700	60	35	s	s	PROPN
bibechana-5700	60	36	,	,	PUNCT
bibechana-5700	60	37	t	t	PROPN
bibechana-5700	60	38	∈	∈	PROPN
bibechana-5700	61	1	[	[	X
bibechana-5700	61	2	a	a	X
bibechana-5700	61	3	,	,	PUNCT
bibechana-5700	61	4	b	b	NOUN
bibechana-5700	61	5	]	]	X
bibechana-5700	61	6	,	,	PUNCT
bibechana-5700	61	7	from	from	ADP
bibechana-5700	61	8	which	which	PRON
bibechana-5700	61	9	we	we	PRON
bibechana-5700	61	10	get	get	VERB
bibechana-5700	61	11	|(kx)(s)|	|(kx)(s)|	PROPN
bibechana-5700	61	12	≤	≤	NOUN
bibechana-5700	61	13	(	(	PUNCT
bibechana-5700	61	14	)	)	PUNCT
bibechana-5700	61	15	(	(	PUNCT
bibechana-5700	61	16	)	)	PUNCT
bibechana-5700	61	17	,	,	PUNCT
bibechana-5700	62	1	b	b	X
bibechana-5700	62	2	a	a	X
bibechana-5700	62	3	k	k	PROPN
bibechana-5700	62	4	s	s	PROPN
bibechana-5700	62	5	t	t	X
bibechana-5700	62	6	x	x	SYM
bibechana-5700	62	7	t	t	PROPN
bibechana-5700	62	8	dt∫	dt∫	NOUN
bibechana-5700	62	9	|	|	ADV
bibechana-5700	63	1	|	|	ADV
bibechana-5700	64	1	|	|	ADV
bibechana-5700	64	2	|	|	ADV
bibechana-5700	64	3	≤	≤	X
bibechana-5700	64	4	µ	µ	NOUN
bibechana-5700	64	5	.	.	PUNCT
bibechana-5700	65	1	||x||	||x||	ADV
bibechana-5700	65	2	.	.	PUNCT
bibechana-5700	66	1	(	(	PUNCT
bibechana-5700	66	2	b	b	X
bibechana-5700	66	3	-	-	PUNCT
bibechana-5700	66	4	a	a	NOUN
bibechana-5700	66	5	)	)	PUNCT
bibechana-5700	66	6	therefore	therefore	ADV
bibechana-5700	66	7	||kx||	||kx||	ADP
bibechana-5700	66	8	≤	≤	NUM
bibechana-5700	66	9	(	(	PUNCT
bibechana-5700	66	10	b	b	NOUN
bibechana-5700	66	11	a)µ	a)µ	NOUN
bibechana-5700	66	12	.	.	PUNCT
bibechana-5700	67	1	||x||	||x||	ADV
bibechana-5700	67	2	.	.	PUNCT
bibechana-5700	68	1	hence	hence	ADV
bibechana-5700	68	2	k	k	PROPN
bibechana-5700	68	3	is	be	AUX
bibechana-5700	68	4	a	a	DET
bibechana-5700	68	5	bounded	bounded	ADJ
bibechana-5700	68	6	operator	operator	NOUN
bibechana-5700	68	7	and	and	CCONJ
bibechana-5700	68	8	therefore	therefore	ADV
bibechana-5700	68	9	,	,	PUNCT
bibechana-5700	68	10	also	also	ADV
bibechana-5700	68	11	a	a	DET
bibechana-5700	68	12	continuous	continuous	ADJ
bibechana-5700	68	13	operator	operator	NOUN
bibechana-5700	68	14	in	in	ADP
bibechana-5700	68	15	other	other	ADJ
bibechana-5700	68	16	words	word	NOUN
bibechana-5700	68	17	,	,	PUNCT
bibechana-5700	68	18	k	k	PROPN
bibechana-5700	68	19	maps	map	VERB
bibechana-5700	68	20	every	every	DET
bibechana-5700	68	21	bounded	bound	VERB
bibechana-5700	68	22	subset	subset	NOUN
bibechana-5700	68	23	of	of	ADP
bibechana-5700	68	24	c[a	c[a	PROPN
bibechana-5700	68	25	,	,	PUNCT
bibechana-5700	68	26	b	b	X
bibechana-5700	68	27	]	]	PUNCT
bibechana-5700	68	28	into	into	ADP
bibechana-5700	68	29	a	a	DET
bibechana-5700	68	30	bounded	bound	VERB
bibechana-5700	68	31	subset	subset	NOUN
bibechana-5700	68	32	of	of	ADP
bibechana-5700	68	33	c[a	c[a	PROPN
bibechana-5700	68	34	,	,	PUNCT
bibechana-5700	68	35	b	b	NOUN
bibechana-5700	68	36	]	]	X
bibechana-5700	68	37	.	.	PUNCT
bibechana-5700	69	1	3	3	X
bibechana-5700	69	2	.	.	X
bibechana-5700	69	3	definition	definition	NOUN
bibechana-5700	69	4	a	a	DET
bibechana-5700	69	5	family	family	NOUN
bibechana-5700	69	6	f	f	NOUN
bibechana-5700	69	7	of	of	ADP
bibechana-5700	69	8	elements	element	NOUN
bibechana-5700	69	9	of	of	ADP
bibechana-5700	69	10	c	c	PROPN
bibechana-5700	69	11	[	[	X
bibechana-5700	69	12	a	a	X
bibechana-5700	69	13	,	,	PUNCT
bibechana-5700	69	14	b	b	NOUN
bibechana-5700	69	15	]	]	PUNCT
bibechana-5700	69	16	is	be	AUX
bibechana-5700	69	17	said	say	VERB
bibechana-5700	69	18	to	to	PART
bibechana-5700	69	19	be	be	AUX
bibechana-5700	69	20	equicontinuous	equicontinuous	ADJ
bibechana-5700	69	21	,	,	PUNCT
bibechana-5700	69	22	if	if	SCONJ
bibechana-5700	69	23	to	to	ADP
bibechana-5700	69	24	each	each	DET
bibechana-5700	69	25	∈>0	∈>0	ADJ
bibechana-5700	69	26	,	,	PUNCT
bibechana-5700	69	27	there	there	PRON
bibechana-5700	69	28	exists	exist	VERB
bibechana-5700	69	29	a	a	DET
bibechana-5700	69	30	δ	δ	NOUN
bibechana-5700	69	31	=	=	PUNCT
bibechana-5700	69	32	δ(∈	δ(∈	NOUN
bibechana-5700	69	33	)	)	PUNCT
bibechana-5700	69	34	>	>	X
bibechana-5700	69	35	0	0	NUM
bibechana-5700	69	36	,	,	PUNCT
bibechana-5700	69	37	s.t	s.t	PROPN
bibechana-5700	69	38	.	.	PROPN
bibechana-5700	69	39	for	for	ADP
bibechana-5700	69	40	all	all	DET
bibechana-5700	69	41	t1	t1	NOUN
bibechana-5700	69	42	,	,	PUNCT
bibechana-5700	69	43	t2	t2	NOUN
bibechana-5700	69	44	∈	∈	PROPN
bibechana-5700	70	1	x,|t1t2|	x,|t1t2|	PUNCT
bibechana-5700	70	2	<	<	X
bibechana-5700	70	3	δ	δ	PROPN
bibechana-5700	70	4	implies	imply	VERB
bibechana-5700	70	5	|	|	ADV
bibechana-5700	70	6	y(t1)-y(t2	y(t1)-y(t2	VERB
bibechana-5700	70	7	)	)	PUNCT
bibechana-5700	71	1	|	|	ADV
bibechana-5700	71	2	<	<	X
bibechana-5700	71	3	∈	∈	PROPN
bibechana-5700	71	4	for	for	ADP
bibechana-5700	71	5	all	all	DET
bibechana-5700	71	6	y∈	y∈	PROPN
bibechana-5700	71	7	f.	f.	PROPN
bibechana-5700	71	8	lemma	lemma	PROPN
bibechana-5700	71	9	:	:	PUNCT
bibechana-5700	71	10	if	if	SCONJ
bibechana-5700	71	11	m	m	NOUN
bibechana-5700	71	12	is	be	AUX
bibechana-5700	71	13	a	a	DET
bibechana-5700	71	14	bounded	bound	VERB
bibechana-5700	71	15	set	set	NOUN
bibechana-5700	71	16	in	in	ADP
bibechana-5700	71	17	c[a	c[a	NUM
bibechana-5700	71	18	,	,	PUNCT
bibechana-5700	71	19	b	b	AUX
bibechana-5700	71	20	]	]	X
bibechana-5700	71	21	then	then	ADV
bibechana-5700	71	22	f	f	PROPN
bibechana-5700	71	23	=	=	PRON
bibechana-5700	71	24	{	{	PUNCT
bibechana-5700	71	25	kx	kx	X
bibechana-5700	71	26	:	:	PUNCT
bibechana-5700	71	27	x	x	X
bibechana-5700	71	28	∈	∈	PROPN
bibechana-5700	71	29	m	m	PRON
bibechana-5700	71	30	}	}	PUNCT
bibechana-5700	71	31	is	be	AUX
bibechana-5700	71	32	a	a	DET
bibechana-5700	71	33	bounded	bounded	ADJ
bibechana-5700	71	34	and	and	CCONJ
bibechana-5700	71	35	equicontinuous	equicontinuous	ADJ
bibechana-5700	71	36	family	family	NOUN
bibechana-5700	71	37	.	.	PUNCT
bibechana-5700	72	1	proof	proof	NOUN
bibechana-5700	72	2	:	:	PUNCT
bibechana-5700	72	3	we	we	PRON
bibechana-5700	72	4	have	have	AUX
bibechana-5700	72	5	seen	see	VERB
bibechana-5700	72	6	above	above	ADP
bibechana-5700	72	7	that	that	PRON
bibechana-5700	72	8	f	f	PROPN
bibechana-5700	72	9	is	be	AUX
bibechana-5700	72	10	bounded	bound	VERB
bibechana-5700	72	11	.	.	PUNCT
bibechana-5700	73	1	now	now	ADV
bibechana-5700	73	2	,	,	PUNCT
bibechana-5700	73	3	it	it	PRON
bibechana-5700	73	4	remains	remain	VERB
bibechana-5700	73	5	to	to	PART
bibechana-5700	73	6	show	show	VERB
bibechana-5700	73	7	that	that	SCONJ
bibechana-5700	73	8	f	f	PROPN
bibechana-5700	73	9	is	be	AUX
bibechana-5700	73	10	equi	equi	NOUN
bibechana-5700	73	11	continuous	continuous	ADJ
bibechana-5700	73	12	.	.	PUNCT
bibechana-5700	74	1	as	as	SCONJ
bibechana-5700	74	2	k	k	PROPN
bibechana-5700	74	3	(	(	PUNCT
bibechana-5700	74	4	s	s	PROPN
bibechana-5700	74	5	,	,	PUNCT
bibechana-5700	74	6	t	t	PROPN
bibechana-5700	74	7	)	)	PUNCT
bibechana-5700	74	8	is	be	AUX
bibechana-5700	74	9	uniformly	uniformly	ADV
bibechana-5700	74	10	continuous	continuous	ADJ
bibechana-5700	74	11	on	on	ADP
bibechana-5700	74	12	[	[	X
bibechana-5700	74	13	a	a	X
bibechana-5700	74	14	,	,	PUNCT
bibechana-5700	74	15	b	b	X
bibechana-5700	74	16	]	]	X
bibechana-5700	74	17	x	x	PUNCT
bibechana-5700	75	1	[	[	X
bibechana-5700	75	2	a	a	X
bibechana-5700	75	3	,	,	PUNCT
bibechana-5700	75	4	b	b	NOUN
bibechana-5700	75	5	]	]	PUNCT
bibechana-5700	75	6	given	give	VERB
bibechana-5700	75	7	∈	∈	PROPN
bibechana-5700	75	8	>	>	X
bibechana-5700	75	9	0	0	NUM
bibechana-5700	75	10	,	,	PUNCT
bibechana-5700	75	11	there	there	PRON
bibechana-5700	75	12	exists	exist	VERB
bibechana-5700	75	13	a	a	DET
bibechana-5700	75	14	δ>0	δ>0	PROPN
bibechana-5700	75	15	s.t	s.t	PROPN
bibechana-5700	75	16	.	.	PROPN
bibechana-5700	75	17	|k(s1	|k(s1	NUM
bibechana-5700	75	18	,	,	PUNCT
bibechana-5700	75	19	t)-k(s2	t)-k(s2	NOUN
bibechana-5700	75	20	,	,	PUNCT
bibechana-5700	75	21	t)|	t)|	NOUN
bibechana-5700	75	22	<	<	X
bibechana-5700	75	23	(	(	PUNCT
bibechana-5700	75	24	)	)	PUNCT
bibechana-5700	75	25	b	b	NOUN
bibechana-5700	76	1	a	a	DET
bibechana-5700	76	2	γ	γ	X
bibechana-5700	76	3	∈	∈	NOUN
bibechana-5700	76	4	−	−	NOUN
bibechana-5700	76	5	for	for	ADP
bibechana-5700	76	6	all	all	DET
bibechana-5700	76	7	t	t	NOUN
bibechana-5700	76	8	∈	∈	PROPN
bibechana-5700	77	1	[	[	X
bibechana-5700	77	2	a	a	X
bibechana-5700	77	3	,	,	PUNCT
bibechana-5700	77	4	b	b	NOUN
bibechana-5700	77	5	]	]	PUNCT
bibechana-5700	77	6	provided	provide	VERB
bibechana-5700	77	7	|s1	|s1	NOUN
bibechana-5700	77	8	–	–	PUNCT
bibechana-5700	77	9	s2|	s2|	X
bibechana-5700	77	10	<	<	X
bibechana-5700	77	11	δ	δ	PROPN
bibechana-5700	77	12	.	.	PUNCT
bibechana-5700	78	1	hence	hence	ADV
bibechana-5700	78	2	|	|	ADV
bibechana-5700	78	3	y(s1)–y(s2)|	y(s1)–y(s2)|	PUNCT
bibechana-5700	78	4	=	=	PUNCT
bibechana-5700	78	5	(	(	PUNCT
bibechana-5700	78	6	)	)	PUNCT
bibechana-5700	78	7	(	(	PUNCT
bibechana-5700	78	8	)	)	PUNCT
bibechana-5700	78	9	(	(	PUNCT
bibechana-5700	78	10	)	)	PUNCT
bibechana-5700	78	11	1	1	NUM
bibechana-5700	78	12	2	2	NUM
bibechana-5700	78	13	,	,	PUNCT
bibechana-5700	78	14	,	,	PUNCT
bibechana-5700	78	15	.	.	PUNCT
bibechana-5700	79	1	b	b	X
bibechana-5700	79	2	a	a	DET
bibechana-5700	79	3	k	k	PROPN
bibechana-5700	79	4	s	s	PROPN
bibechana-5700	79	5	t	t	PROPN
bibechana-5700	80	1	k	k	PROPN
bibechana-5700	80	2	s	s	PROPN
bibechana-5700	80	3	t	t	X
bibechana-5700	80	4	x	x	SYM
bibechana-5700	80	5	t	t	PROPN
bibechana-5700	80	6	dt	dt	PROPN
bibechana-5700	80	7	−	−	PROPN
bibechana-5700	80	8	∫|	∫|	NOUN
bibechana-5700	80	9	|	|	ADV
bibechana-5700	80	10	≤	≤	PROPN
bibechana-5700	80	11	(	(	PUNCT
bibechana-5700	80	12	)	)	PUNCT
bibechana-5700	80	13	(	(	PUNCT
bibechana-5700	80	14	)	)	PUNCT
bibechana-5700	80	15	(	(	PUNCT
bibechana-5700	80	16	)	)	PUNCT
bibechana-5700	80	17	1	1	NUM
bibechana-5700	80	18	2	2	NUM
bibechana-5700	80	19	,	,	PUNCT
bibechana-5700	80	20	,	,	PUNCT
bibechana-5700	80	21	b	b	PROPN
bibechana-5700	80	22	a	a	X
bibechana-5700	81	1	k	k	PROPN
bibechana-5700	81	2	s	s	PROPN
bibechana-5700	81	3	t	t	PROPN
bibechana-5700	81	4	s	s	PROPN
bibechana-5700	81	5	t	t	NOUN
bibechana-5700	81	6	x	x	SYM
bibechana-5700	81	7	t	t	NOUN
bibechana-5700	82	1	dt−∫	dt−∫	PRON
bibechana-5700	82	2	|	|	ADV
bibechana-5700	83	1	|	|	ADV
bibechana-5700	83	2	|	|	ADV
bibechana-5700	84	1	|	|	ADV
bibechana-5700	84	2	<	<	X
bibechana-5700	84	3	(	(	PUNCT
bibechana-5700	84	4	)	)	PUNCT
bibechana-5700	84	5	(	(	PUNCT
bibechana-5700	84	6	)	)	PUNCT
bibechana-5700	84	7	b	b	NOUN
bibechana-5700	84	8	a	a	DET
bibechana-5700	84	9	b	b	NOUN
bibechana-5700	84	10	a	a	DET
bibechana-5700	84	11	γ	γ	X
bibechana-5700	84	12	γ	γ	X
bibechana-5700	84	13	∈	∈	PROPN
bibechana-5700	84	14	−	−	NOUN
bibechana-5700	84	15	−	−	PROPN
bibechana-5700	84	16	=	=	SYM
bibechana-5700	84	17	∈	∈	PROPN
bibechana-5700	84	18	,	,	PUNCT
bibechana-5700	84	19	provided	provide	VERB
bibechana-5700	84	20	|s1	|s1	NOUN
bibechana-5700	84	21	-	-	PUNCT
bibechana-5700	84	22	s2|<δ	s2|<δ	NOUN
bibechana-5700	84	23	hence	hence	ADV
bibechana-5700	84	24	f	f	PROPN
bibechana-5700	84	25	is	be	AUX
bibechana-5700	84	26	equicontinuous	equicontinuous	ADJ
bibechana-5700	84	27	.	.	PUNCT
bibechana-5700	85	1	for	for	ADP
bibechana-5700	85	2	further	far	ADV
bibechana-5700	85	3	we	we	PRON
bibechana-5700	85	4	need	need	VERB
bibechana-5700	85	5	the	the	DET
bibechana-5700	85	6	arzela	arzela	PROPN
bibechana-5700	85	7	-	-	PUNCT
bibechana-5700	85	8	ascoli	ascoli	PROPN
bibechana-5700	85	9	's	's	PART
bibechana-5700	85	10	theorem	theorem	NOUN
bibechana-5700	85	11	.	.	PUNCT
bibechana-5700	86	1	arzela	arzela	PROPN
bibechana-5700	86	2	–	–	PUNCT
bibechana-5700	86	3	ascoli	ascoli	PROPN
bibechana-5700	86	4	's	's	PART
bibechana-5700	86	5	theorem	theorem	NOUN
bibechana-5700	86	6	if	if	SCONJ
bibechana-5700	86	7	f	f	PROPN
bibechana-5700	86	8	is	be	AUX
bibechana-5700	86	9	a	a	DET
bibechana-5700	86	10	bounded	bounded	ADJ
bibechana-5700	86	11	and	and	CCONJ
bibechana-5700	86	12	equicontinuous	equicontinuous	ADJ
bibechana-5700	86	13	family	family	NOUN
bibechana-5700	86	14	in	in	ADP
bibechana-5700	86	15	c	c	PROPN
bibechana-5700	86	16	[	[	X
bibechana-5700	86	17	a	a	X
bibechana-5700	86	18	,	,	PUNCT
bibechana-5700	86	19	b	b	NOUN
bibechana-5700	86	20	]	]	X
bibechana-5700	86	21	then	then	ADV
bibechana-5700	86	22	every	every	DET
bibechana-5700	86	23	sequence	sequence	NOUN
bibechana-5700	86	24	of	of	ADP
bibechana-5700	86	25	elements	element	NOUN
bibechana-5700	86	26	of	of	ADP
bibechana-5700	86	27	f	f	PROPN
bibechana-5700	86	28	contains	contain	VERB
bibechana-5700	86	29	a	a	DET
bibechana-5700	86	30	convergent	convergent	NOUN
bibechana-5700	86	31	subsequence[3	subsequence[3	NOUN
bibechana-5700	86	32	]	]	PUNCT
bibechana-5700	86	33	.	.	PUNCT
bibechana-5700	87	1	from	from	ADP
bibechana-5700	87	2	arzela	arzela	PROPN
bibechana-5700	87	3	–	–	PUNCT
bibechana-5700	87	4	ascoli	ascoli	PROPN
bibechana-5700	87	5	's	's	PART
bibechana-5700	87	6	theorem	theorem	NOUN
bibechana-5700	87	7	it	it	PRON
bibechana-5700	87	8	follows	follow	VERB
bibechana-5700	87	9	that	that	SCONJ
bibechana-5700	87	10	the	the	DET
bibechana-5700	87	11	image	image	NOUN
bibechana-5700	87	12	sequence	sequence	NOUN
bibechana-5700	87	13	kx1	kx1	PROPN
bibechana-5700	87	14	,	,	PUNCT
bibechana-5700	87	15	kx2	kx2	PROPN
bibechana-5700	87	16	,	,	PUNCT
bibechana-5700	87	17	kx3	kx3	NOUN
bibechana-5700	87	18	,	,	PUNCT
bibechana-5700	87	19	…	…	PUNCT
bibechana-5700	87	20	of	of	ADP
bibechana-5700	87	21	a	a	DET
bibechana-5700	87	22	bounded	bounded	ADJ
bibechana-5700	87	23	sequence	sequence	NOUN
bibechana-5700	87	24	is	be	AUX
bibechana-5700	87	25	c	c	NOUN
bibechana-5700	88	1	[	[	X
bibechana-5700	88	2	a	a	X
bibechana-5700	88	3	,	,	PUNCT
bibechana-5700	88	4	b	b	X
bibechana-5700	88	5	]	]	PUNCT
bibechana-5700	88	6	contains	contain	VERB
bibechana-5700	88	7	a	a	DET
bibechana-5700	88	8	convergent	convergent	NOUN
bibechana-5700	88	9	sebsequence	sebsequence	NOUN
bibechana-5700	88	10	.	.	PUNCT
bibechana-5700	89	1	riesz	riesz	PROPN
bibechana-5700	89	2	has	have	AUX
bibechana-5700	89	3	constructed	construct	VERB
bibechana-5700	89	4	the	the	DET
bibechana-5700	89	5	theory	theory	NOUN
bibechana-5700	89	6	of	of	ADP
bibechana-5700	89	7	fredholm	fredholm	ADJ
bibechana-5700	89	8	integral	integral	ADJ
bibechana-5700	89	9	equations	equation	NOUN
bibechana-5700	89	10	on	on	ADP
bibechana-5700	89	11	this	this	DET
bibechana-5700	89	12	property	property	NOUN
bibechana-5700	89	13	of	of	ADP
bibechana-5700	89	14	k[6	k[6	PROPN
bibechana-5700	89	15	]	]	PUNCT
bibechana-5700	89	16	.	.	PUNCT
bibechana-5700	90	1	4	4	X
bibechana-5700	90	2	.	.	X
bibechana-5700	90	3	definition	definition	NOUN
bibechana-5700	90	4	if	if	SCONJ
bibechana-5700	90	5	e	e	PROPN
bibechana-5700	90	6	and	and	CCONJ
bibechana-5700	90	7	f	f	PROPN
bibechana-5700	90	8	are	be	AUX
bibechana-5700	90	9	normed	norme	VERB
bibechana-5700	90	10	linear	linear	PROPN
bibechana-5700	90	11	spaces	space	NOUN
bibechana-5700	90	12	then	then	ADV
bibechana-5700	90	13	a	a	DET
bibechana-5700	90	14	map	map	NOUN
bibechana-5700	90	15	k∈l(e	k∈l(e	PROPN
bibechana-5700	90	16	,	,	PUNCT
bibechana-5700	90	17	f	f	X
bibechana-5700	90	18	)	)	PUNCT
bibechana-5700	90	19	is	be	AUX
bibechana-5700	90	20	called	call	VERB
bibechana-5700	90	21	completely	completely	ADV
bibechana-5700	90	22	continuous	continuous	ADJ
bibechana-5700	90	23	if	if	SCONJ
bibechana-5700	90	24	for	for	ADP
bibechana-5700	90	25	every	every	DET
bibechana-5700	90	26	bounded	bounded	ADJ
bibechana-5700	90	27	sequence	sequence	NOUN
bibechana-5700	90	28	{	{	PUNCT
bibechana-5700	90	29	xn	xn	NOUN
bibechana-5700	90	30	}	}	PUNCT
bibechana-5700	90	31	in	in	ADP
bibechana-5700	90	32	e	e	NOUN
bibechana-5700	90	33	,	,	PUNCT
bibechana-5700	90	34	the	the	DET
bibechana-5700	90	35	image	image	NOUN
bibechana-5700	90	36	sequence	sequence	NOUN
bibechana-5700	90	37	{	{	PUNCT
bibechana-5700	90	38	kxn	kxn	PROPN
bibechana-5700	90	39	}	}	PUNCT
bibechana-5700	90	40	in	in	ADP
bibechana-5700	90	41	f	f	PROPN
bibechana-5700	90	42	has	have	VERB
bibechana-5700	90	43	a	a	DET
bibechana-5700	90	44	convergent	convergent	NOUN
bibechana-5700	90	45	sebsequence	sebsequence	NOUN
bibechana-5700	90	46	.	.	PUNCT
bibechana-5700	91	1	lemma	lemma	PROPN
bibechana-5700	91	2	:	:	PUNCT
bibechana-5700	91	3	a	a	DET
bibechana-5700	91	4	completely	completely	ADV
bibechana-5700	91	5	continuous	continuous	ADJ
bibechana-5700	91	6	linear	linear	NOUN
bibechana-5700	91	7	operator	operator	NOUN
bibechana-5700	91	8	k	k	PROPN
bibechana-5700	91	9	is	be	AUX
bibechana-5700	91	10	continuous	continuous	ADJ
bibechana-5700	91	11	.	.	PUNCT
bibechana-5700	92	1	suppose	suppose	VERB
bibechana-5700	92	2	if	if	SCONJ
bibechana-5700	92	3	k	k	PROPN
bibechana-5700	92	4	is	be	AUX
bibechana-5700	92	5	not	not	PART
bibechana-5700	92	6	continuous	continuous	ADJ
bibechana-5700	92	7	,	,	PUNCT
bibechana-5700	92	8	k	k	PROPN
bibechana-5700	92	9	is	be	AUX
bibechana-5700	92	10	not	not	PART
bibechana-5700	92	11	bounded	bound	VERB
bibechana-5700	92	12	,	,	PUNCT
bibechana-5700	92	13	sup	sup	INTJ
bibechana-5700	92	14	||kxn||	||kxn||	PUNCT
bibechana-5700	92	15	=	=	SYM
bibechana-5700	92	16	∞	∞	PROPN
bibechana-5700	92	17	,	,	PUNCT
bibechana-5700	92	18	hence	hence	ADV
bibechana-5700	92	19	there	there	PRON
bibechana-5700	92	20	exists	exist	VERB
bibechana-5700	92	21	a	a	DET
bibechana-5700	92	22	sequence	sequence	NOUN
bibechana-5700	92	23	{	{	PUNCT
bibechana-5700	92	24	xn	xn	NUM
bibechana-5700	92	25	}	}	PUNCT
bibechana-5700	92	26	with	with	ADP
bibechana-5700	92	27	||xn||≤1	||xn||≤1	PROPN
bibechana-5700	92	28	and	and	CCONJ
bibechana-5700	92	29	||kxn||→∞	||kxn||→∞	PROPN
bibechana-5700	92	30	which	which	PRON
bibechana-5700	92	31	contradicts	contradict	VERB
bibechana-5700	92	32	that	that	SCONJ
bibechana-5700	92	33	k	k	PROPN
bibechana-5700	92	34	is	be	AUX
bibechana-5700	92	35	completely	completely	ADV
bibechana-5700	92	36	continuous	continuous	ADJ
bibechana-5700	92	37	.	.	PUNCT
bibechana-5700	93	1	but	but	CCONJ
bibechana-5700	93	2	every	every	DET
bibechana-5700	93	3	continuous	continuous	ADJ
bibechana-5700	93	4	operator	operator	NOUN
bibechana-5700	93	5	is	be	AUX
bibechana-5700	93	6	not	not	PART
bibechana-5700	93	7	completely	completely	ADV
bibechana-5700	93	8	continuous	continuous	ADJ
bibechana-5700	93	9	.	.	PUNCT
bibechana-5700	94	1	for	for	ADP
bibechana-5700	94	2	example	example	NOUN
bibechana-5700	94	3	,	,	PUNCT
bibechana-5700	94	4	the	the	DET
bibechana-5700	94	5	identity	identity	NOUN
bibechana-5700	94	6	map	map	NOUN
bibechana-5700	94	7	i	i	PRON
bibechana-5700	94	8	on	on	ADP
bibechana-5700	94	9	an	an	DET
bibechana-5700	94	10	infinite	infinite	ADJ
bibechana-5700	94	11	dimensional	dimensional	ADJ
bibechana-5700	94	12	normed	norme	VERB
bibechana-5700	94	13	linear	linear	ADJ
bibechana-5700	94	14	space	space	NOUN
bibechana-5700	94	15	is	be	AUX
bibechana-5700	94	16	continuous	continuous	ADJ
bibechana-5700	94	17	but	but	CCONJ
bibechana-5700	94	18	not	not	PART
bibechana-5700	94	19	completely	completely	ADV
bibechana-5700	94	20	continuous	continuous	ADJ
bibechana-5700	94	21	[	[	X
bibechana-5700	94	22	2,5	2,5	NUM
bibechana-5700	94	23	]	]	PUNCT
bibechana-5700	94	24	.	.	PUNCT
bibechana-5700	95	1	g.k	g.k	PROPN
bibechana-5700	95	2	.	.	PROPN
bibechana-5700	95	3	palei	palei	PROPN
bibechana-5700	95	4	and	and	CCONJ
bibechana-5700	95	5	n.p	n.p	PROPN
bibechana-5700	95	6	.	.	PROPN
bibechana-5700	95	7	sah	sah	PROPN
bibechana-5700	95	8	/	/	SYM
bibechana-5700	95	9	bibechana	bibechana	PROPN
bibechana-5700	95	10	8	8	NUM
bibechana-5700	95	11	(	(	PUNCT
bibechana-5700	95	12	2012	2012	NUM
bibechana-5700	95	13	)	)	PUNCT
bibechana-5700	95	14	127	127	NUM
bibechana-5700	95	15	-	-	SYM
bibechana-5700	95	16	130	130	NUM
bibechana-5700	95	17	:	:	PUNCT
bibechana-5700	95	18	bmhss	bmhss	PROPN
bibechana-5700	95	19	,	,	PUNCT
bibechana-5700	95	20	p.130	p.130	NOUN
bibechana-5700	95	21	theorem	theorem	NOUN
bibechana-5700	95	22	:	:	PUNCT
bibechana-5700	95	23	a	a	DET
bibechana-5700	95	24	continuous	continuous	ADJ
bibechana-5700	95	25	operator	operator	NOUN
bibechana-5700	95	26	k	k	PROPN
bibechana-5700	95	27	of	of	ADP
bibechana-5700	95	28	finite	finite	PROPN
bibechana-5700	95	29	rank	rank	NOUN
bibechana-5700	95	30	is	be	AUX
bibechana-5700	95	31	completely	completely	ADV
bibechana-5700	95	32	continuous	continuous	ADJ
bibechana-5700	95	33	.	.	PUNCT
bibechana-5700	96	1	proof	proof	NOUN
bibechana-5700	96	2	:	:	PUNCT
bibechana-5700	96	3	if	if	SCONJ
bibechana-5700	96	4	{	{	PUNCT
bibechana-5700	96	5	xn	xn	X
bibechana-5700	96	6	}	}	PUNCT
bibechana-5700	96	7	is	be	AUX
bibechana-5700	96	8	a	a	DET
bibechana-5700	96	9	bounded	bounded	ADJ
bibechana-5700	96	10	sequence	sequence	NOUN
bibechana-5700	96	11	in	in	ADP
bibechana-5700	96	12	e	e	NOUN
bibechana-5700	96	13	,	,	PUNCT
bibechana-5700	96	14	then	then	ADV
bibechana-5700	96	15	the	the	DET
bibechana-5700	96	16	image	image	NOUN
bibechana-5700	96	17	sequence	sequence	NOUN
bibechana-5700	96	18	{	{	PUNCT
bibechana-5700	96	19	kxn	kxn	PROPN
bibechana-5700	96	20	}	}	PUNCT
bibechana-5700	96	21	in	in	ADP
bibechana-5700	96	22	f	f	PROPN
bibechana-5700	96	23	is	be	AUX
bibechana-5700	96	24	bounded	bound	VERB
bibechana-5700	96	25	.	.	PUNCT
bibechana-5700	97	1	now	now	ADV
bibechana-5700	97	2	,	,	PUNCT
bibechana-5700	97	3	since	since	SCONJ
bibechana-5700	97	4	b(k	b(k	PROPN
bibechana-5700	97	5	)	)	PUNCT
bibechana-5700	97	6	i.e.	i.e.	X
bibechana-5700	97	7	the	the	DET
bibechana-5700	97	8	image	image	NOUN
bibechana-5700	97	9	space	space	NOUN
bibechana-5700	97	10	of	of	ADP
bibechana-5700	97	11	k	k	PROPN
bibechana-5700	97	12	is	be	AUX
bibechana-5700	97	13	finite	finite	ADJ
bibechana-5700	97	14	dimensional	dimensional	ADJ
bibechana-5700	97	15	,	,	PUNCT
bibechana-5700	97	16	hence	hence	ADV
bibechana-5700	97	17	b(k	b(k	PROPN
bibechana-5700	97	18	)	)	PUNCT
bibechana-5700	97	19	is	be	AUX
bibechana-5700	97	20	complete	complete	ADJ
bibechana-5700	97	21	.	.	PUNCT
bibechana-5700	98	1	hence	hence	ADV
bibechana-5700	98	2	applying	apply	VERB
bibechana-5700	98	3	bolzano	bolzano	NOUN
bibechana-5700	98	4	.	.	PUNCT
bibechana-5700	99	1	weierstrass	weierstrass	PROPN
bibechana-5700	99	2	theorem	theorem	VERB
bibechana-5700	99	3	it	it	PRON
bibechana-5700	99	4	follows	follow	VERB
bibechana-5700	99	5	that	that	SCONJ
bibechana-5700	99	6	there	there	PRON
bibechana-5700	99	7	exists	exist	VERB
bibechana-5700	99	8	a	a	DET
bibechana-5700	99	9	convergent	convergent	NOUN
bibechana-5700	99	10	sebsequence	sebsequence	NOUN
bibechana-5700	99	11	{	{	PUNCT
bibechana-5700	99	12	kxn	kxn	PROPN
bibechana-5700	99	13	}	}	PUNCT
bibechana-5700	99	14	.	.	PUNCT
bibechana-5700	100	1	reference	reference	NOUN
bibechana-5700	101	1	[	[	X
bibechana-5700	101	2	1	1	NUM
bibechana-5700	101	3	]	]	X
bibechana-5700	101	4	bruce	bruce	PROPN
bibechana-5700	101	5	biackadar	biackadar	PROPN
bibechana-5700	101	6	,	,	PUNCT
bibechana-5700	101	7	operator	operator	NOUN
bibechana-5700	101	8	algebras	algebra	NOUN
bibechana-5700	101	9	,	,	PUNCT
bibechana-5700	101	10	encyelopedia	encyelopedia	NOUN
bibechana-5700	101	11	of	of	ADP
bibechana-5700	101	12	mathematical	mathematical	ADJ
bibechana-5700	101	13	sciences	science	NOUN
bibechana-5700	101	14	,	,	PUNCT
bibechana-5700	101	15	springer	springer	NOUN
bibechana-5700	101	16	–	–	PUNCT
bibechana-5700	101	17	verlag	verlag	NOUN
bibechana-5700	101	18	,	,	PUNCT
bibechana-5700	101	19	2005	2005	NUM
bibechana-5700	101	20	.	.	PUNCT
bibechana-5700	102	1	[	[	X
bibechana-5700	102	2	2	2	X
bibechana-5700	102	3	]	]	X
bibechana-5700	102	4	john	john	PROPN
bibechana-5700	102	5	b	b	PROPN
bibechana-5700	102	6	conway	conway	PROPN
bibechana-5700	102	7	,	,	PUNCT
bibechana-5700	102	8	a	a	DET
bibechana-5700	102	9	course	course	NOUN
bibechana-5700	102	10	on	on	ADP
bibechana-5700	102	11	funtional	funtional	ADJ
bibechana-5700	102	12	analysis	analysis	NOUN
bibechana-5700	102	13	springer	springer	NOUN
bibechana-5700	102	14	–	–	PUNCT
bibechana-5700	102	15	verlag	verlag	NOUN
bibechana-5700	102	16	,	,	PUNCT
bibechana-5700	102	17	1985	1985	NUM
bibechana-5700	102	18	.	.	PUNCT
bibechana-5700	103	1	[	[	X
bibechana-5700	103	2	3	3	X
bibechana-5700	103	3	]	]	X
bibechana-5700	103	4	s.	s.	PROPN
bibechana-5700	103	5	goldberg	goldberg	PROPN
bibechana-5700	103	6	,	,	PUNCT
bibechana-5700	103	7	unbounded	unbounded	ADJ
bibechana-5700	103	8	linear	linear	PROPN
bibechana-5700	103	9	operators	operator	NOUN
bibechana-5700	103	10	,	,	PUNCT
bibechana-5700	103	11	mc	mc	PROPN
bibechana-5700	103	12	.	.	PROPN
bibechana-5700	103	13	graw	graw	PROPN
bibechana-5700	103	14	hill	hill	PROPN
bibechana-5700	103	15	,	,	PUNCT
bibechana-5700	103	16	new	new	ADJ
bibechana-5700	103	17	yorks	yorks	PROPN
bibechana-5700	103	18	,	,	PUNCT
bibechana-5700	103	19	1966	1966	NUM
bibechana-5700	103	20	.	.	PUNCT
bibechana-5700	104	1	[	[	X
bibechana-5700	104	2	4	4	NUM
bibechana-5700	104	3	]	]	X
bibechana-5700	104	4	k	k	X
bibechana-5700	104	5	hvedelidge	hvedelidge	PROPN
bibechana-5700	104	6	:	:	PUNCT
bibechana-5700	104	7	fredholm	fredholm	NOUN
bibechana-5700	104	8	theorem	theorem	NOUN
bibechana-5700	104	9	,	,	PUNCT
bibechana-5700	104	10	encyclopedia	encyclopedia	NOUN
bibechana-5700	104	11	of	of	ADP
bibechana-5700	104	12	maths	math	NOUN
bibechana-5700	104	13	,	,	PUNCT
bibechana-5700	104	14	springer	springer	NOUN
bibechana-5700	104	15	–	–	PUNCT
bibechana-5700	104	16	verlag	verlag	NOUN
bibechana-5700	104	17	,	,	PUNCT
bibechana-5700	104	18	2001	2001	NUM
bibechana-5700	104	19	[	[	X
bibechana-5700	104	20	5	5	NUM
bibechana-5700	104	21	]	]	PUNCT
bibechana-5700	104	22	g.	g.	NOUN
bibechana-5700	104	23	kothe	kothe	PROPN
bibechana-5700	104	24	,	,	PUNCT
bibechana-5700	104	25	top	top	ADJ
bibechana-5700	104	26	,	,	PUNCT
bibechana-5700	104	27	vector	vector	NOUN
bibechana-5700	104	28	space	space	NOUN
bibechana-5700	104	29	,	,	PUNCT
bibechana-5700	104	30	i	i	PRON
bibechana-5700	104	31	and	and	CCONJ
bibechana-5700	104	32	ii	ii	PROPN
bibechana-5700	104	33	springer	springer	NOUN
bibechana-5700	104	34	verlag	verlag	PROPN
bibechana-5700	104	35	,	,	PUNCT
bibechana-5700	104	36	1969	1969	NUM
bibechana-5700	104	37	.	.	PUNCT
bibechana-5700	105	1	[	[	X
bibechana-5700	105	2	6	6	NUM
bibechana-5700	105	3	]	]	PUNCT
bibechana-5700	105	4	alena	alena	PROPN
bibechana-5700	105	5	pietro	pietro	VERB
bibechana-5700	105	6	a	a	DET
bibechana-5700	105	7	characterization	characterization	NOUN
bibechana-5700	105	8	of	of	ADP
bibechana-5700	105	9	riesz	riesz	NOUN
bibechana-5700	105	10	operators	operator	NOUN
bibechana-5700	105	11	:	:	PUNCT
bibechana-5700	105	12	in	in	ADP
bibechana-5700	105	13	the	the	DET
bibechana-5700	105	14	journal	journal	NOUN
bibechana-5700	105	15	of	of	ADP
bibechana-5700	105	16	"	"	PUNCT
bibechana-5700	105	17	mathematiche	mathematiche	NOUN
bibechana-5700	105	18	zeitschrift	zeitschrift	NOUN
bibechana-5700	105	19	,	,	PUNCT
bibechana-5700	105	20	springer	springer	NOUN
bibechana-5700	105	21	-	-	PUNCT
bibechana-5700	105	22	berlin	berlin	PROPN
bibechana-5700	105	23	,	,	PUNCT
bibechana-5700	105	24	2005	2005	NUM
bibechana-5700	105	25	.	.	PUNCT
bibechana-5700	106	1	[	[	X
bibechana-5700	106	2	7	7	X
bibechana-5700	106	3	]	]	X
bibechana-5700	106	4	a.g	a.g	PROPN
bibechana-5700	106	5	.	.	PROPN
bibechana-5700	106	6	ramm	ramm	PROPN
bibechana-5700	106	7	,	,	PUNCT
bibechana-5700	106	8	a	a	DET
bibechana-5700	106	9	simple	simple	ADJ
bibechana-5700	106	10	proof	proof	NOUN
bibechana-5700	106	11	of	of	ADP
bibechana-5700	106	12	the	the	DET
bibechana-5700	106	13	fredholm	fredholm	NOUN
bibechana-5700	106	14	alternative	alternative	NOUN
bibechana-5700	106	15	and	and	CCONJ
bibechana-5700	106	16	characterization	characterization	NOUN
bibechana-5700	106	17	of	of	ADP
bibechana-5700	106	18	the	the	DET
bibechana-5700	106	19	fredholm	fredholm	NOUN
bibechana-5700	106	20	operators	operator	NOUN
bibechana-5700	106	21	,	,	PUNCT
bibechana-5700	106	22	american	american	PROPN
bibechana-5700	106	23	mathematical	mathematical	ADJ
bibechana-5700	106	24	monthly	monthly	ADJ
bibechana-5700	106	25	journal	journal	NOUN
bibechana-5700	106	26	p.815	p.815	NOUN
bibechana-5700	106	27	;	;	PUNCT
bibechana-5700	106	28	2001	2001	NUM
bibechana-5700	106	29	.	.	PUNCT